MEK 1/2 Inhibitor Selumetinib (AZD6244 Hydrogen Sulfate) in Adults With Neurofibromatosis Type 1 (NF1) and Inoperable Plexiform Neurofibromas

* INCLUSION CRITERIA: * Patients must have positive genetic testing for NF1 in a CLIA certified laboratory or a diagnosis of NF1 based on clinical NIH consensus criteria of at least one other diagnostic criterion in addition to the presence of a PN. NF1 mutation analysis will be performed on germline DNA. Histologic confirmation of tumor is not necessary in the presence of consistent clinical and imaging findings, but should be considered if malignant transformation of a PN is clinically suspected. Additional criteria are as follows: * Six or more cafe-au-lait macules (\>=0.5cm in prepubertal subjects or \>=1.5 cm in post pubertal subjects) * Freckling in axilla or groin * Optic glioma * Two or more Lisch nodules * A distinctive bony lesion (dysplasia of the sphenoid bone or dysplasia or thinning of long bone cortex) * A first-degree relative with NF1 * Measurable disease: Patients must have at least one measurable PN, defined as a lesion of at least 3 cm measured in one dimension. Patients who underwent surgery for resection of a PN are eligible provided the PN was incompletely resected and is measurable as per criteria above. Measurability and suitability for volumetric MRI analysis of the target PN must be confirmed with the NCI POB prior to enrolling a patient. The target PN will be defined as the clinically most relevant PN, which has to be amenable to volumetric MRI analysis. PN will be classified as typical PN versus nodular PN versus solitary nodular PN prior to enrollment * The PN must be inoperable, defined as a PN that cannot be surgically completely removed without risk for substantial morbidity due to: encasement of or close proximity to vital structures, invasiveness, or high vascularity of the PN. The PN either causes morbidity or it is growing and has the potential to cause morbidity such as (but not limited to): Head and neck lesions that could compromise the airway or great vessels, paraspinal lesions that can cause myelopathy, brachial or lumbar plexus lesions that could cause nerve compression and loss of function, lesions that could result in major deformity (e.g., orbital lesions) or are significantly disfiguring, and lesions of the extremity that cause limb hypertrophy or loss of function or pain. PN growth will be defined as a \>=20% increase in PN volume within approximately 3 years prior to enrollment on this trial. * Patients must have a PN amenable to a percutaneous biopsy to participate in the biopsy portion of this study, and must be willing to undergo pre-, and on treatment tumor biopsies. There should be no contraindication for serial biopsies. NOTE: Up to 10 patients who meet all criteria, but have PN which cannot be biopsied safely, will be eligible for the treatment portion of the study. * Must be able to undergo serial MRI scans for response evaluation * Age \>=18 years * ECOG performance status \<=2 (Patients who are wheelchair bound because of paralysis secondary to a plexiform neurofibroma should be considered ambulatory when they are up in their wheelchair. Similarly, patients with limited mobility secondary to need for mechanical support (such as an airway PN requiring tracheostomy or CPAP) will also be considered ambulatory for the purpose of the study.) --ECOG Performance Status:\* * Grade/ECOG * 0 Fully active, able to carry on all pre-disease performance without restriction * 1 Restricted in physically strenuous activity but ambulatory and able to carry out work of a light or sedentary nature, e.g., light house work, office work * 2 Ambulatory and capable of all self-care but unable to carry out any work activities. Up and about more than 50% of waking hours * 3 Capable of only limited self-care, confined to bed or chair more than 50% of waking hours * 4 Completely disabled. Cannot carry on any self-care. Totally confined to bed or chair * 5 Dead * As published in Am. J. Clin. Oncol.: Oken, M.M., Creech, R.H., Tormey, D.C., Horton, J., Davis, T.E., McFadden, E.T., Carbone, P.P.: Toxicity And Response Criteria Of The Eastern Cooperative Oncology Group. Am J Clin Oncol 5:649-655, 1982. * Patients must have normal organ and marrow function as defined below: * Hemoglobin \>=10 g/dL (not requiring RBC transfusions) * Absolute neutrophil count \>=1,500/mcL * Platelets \>=100,000/mcL (not requiring platelet transfusions) * Total bilirubin \<=1.5 upper limit of normal (ULN), with the exception of patients with Gilbert Syndrome * ALT(SGPT) \& AST(SGOT) \<=3.0 X ULN * Creatinine \<=upper limit of normal institutional limits * OR * Creatinine clearance \>=60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Hematologic parameters for patients undergoing biopsy only: Patients should have INR \<=1.4 and PTT \<=40 seconds (unless due to lupus anticoagulant). In patients not meeting these parameters, clearance by hematology will be required prior to undergoing a biopsy. * Cardiac Function: Normal ejection fraction (ECHO) \>=53% (if a range is given then the upper value of the range will be used) or cardiac MRI; QTcF \<=450 msec. * Ability of subject or Legally Authorized Representative (LAR)) to understand and the willingness to sign a written informed consent document. * Willingness to avoid excessive sun exposure and use adequate sunscreen protection if sun exposure is anticipated. * Willingness to avoid the ingestion of grapefruit and Seville oranges (as well as other products containing these fruits, e.g. grapefruit juice or marmalade) during the study. * Prior therapy: Patients with NF1 will only be eligible if complete tumor resection is not considered to be feasible without substantial risk or morbidity, or if a patient with a surgical option refuses surgery. * Since there is no standard effective chemotherapy for patients with NF1 and PN, patients may be treated on this trial without having received prior medical therapy directed at their PN. * Since selumetinib is not expected to cause substantial myelosuppression, there will be no limit to number of prior myelosuppressive regimen for PN or other tumor manifestations associated with NF1 such as optic glioma. * Patients who have received previous investigational agents or biologic therapy, such as tipifarnib, pirfenidone, Peg-Intron, sorafenib, or other VEGFR inhibitors are eligible for enrollment. * Growth factors that support platelet or white cell number or function must not have been administered within the past 7 days and are not permitted while on the study. * At least 6 weeks must have elapsed prior to enrollment since the patient received any prior radiation therapy, and no prior radiation therapy should have been directed at the target PN. * At least 4 weeks must have elapsed since receiving medical therapy directed at the PN. * At least 4 weeks must have elapsed since any surgeries, with evidence of completed wound healing. * Patients who received prior medical therapy for their PN must have recovered from the acute toxic effects of all prior therapy to \<= grade 1 before entering this study. * Informed Consent: Diagnostic or laboratory studies performed exclusively to determine eligibility for this trial must only be done after obtaining written informed consent from all patients, which can be accomplished using the screening consent for this protocol. Studies or procedures that were performed for clinical indications (not exclusively to determine eligibility) may be used for screening or baseline values even if the studies were done before informed consent was obtained, if the patient agrees. EXCLUSION CRITERIA: * Patients who are receiving any other investigational agents, or have received an investigational agent within the past 30 days. * May not have a NF1 related tumor such as optic pathway glioma or malignant peripheral nerve sheath tumor, which requires treatment with chemotherapy or surgery. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active bleeding diatheses or renal transplant, including any patient known to have hepatitis B, hepatitis C or human immunodeficiency virus (HIV), or psychiatric illness/social situations that would limit compliance with study requirements. Patients with HIV who have adequate CD4 counts and who have no requirement for antiviral therapy will be eligible. * Pregnant or breast-feeding females are excluded due to potential risks of fetal and teratogenic adverse events of an investigational agent. Males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method. Abstinence is an acceptable method of birth control. * Prior treatment with selumetinib or another specific MEK 1/2 inhibitor. * Supplementation with vitamin E greater than 100% of the daily recommended dose. * Inability to swallow capsules, since capsules cannot be crushed or broken. * Inability to undergo MRI and/or contraindication for MRI examinations following the MRI protocol. Prosthesis or orthopedic or dental braces that would interfere with volumetric analysis of target PN on MRI. * Refractory nausea and vomiting, chronic gastrointestinal diseases (e.g., inflammatory bowel disease), or significant bowel resection that would preclude adequate absorption. * Uncontrolled hypertension (despite medical therapy); blood pressure should be \<140/90 in accordance with American Heart Association definition of hypertension. * While not an exclusion criterion, unless clinically indicated, patients should avoid taking other additional non-study medications that may interfere with the study medications. In particular, patients should avoid medications that are known to either induce or inhibit the activity of hepatic microsomal isoenzymes CYP1A2, CYP2C19 and CYP3A4, as this may interfere with the metabolism of selumetinib. * Known Cardiac Disorder, including: * Known inherited coronary disease * Symptomatic heart failure (NYHA Class II-IV prior or current cardiomyopathy, or severe valvular heart disease) * Current cardiomyopathy * Severe valvular heart disease * Atrial fibrillation * Ejection fraction (ECHO) \<53% * QTcF \>450 msec * Known Ophthalmologic conditions, such as: * Current or past history of central serous retinopathy * Current or past history of retinal vein occlusion * Known intraocular pressure (IOP) \> 21 mmHg (or ULN adjusted by age) or uncontrolled glaucoma (irrespective of IOP). Patients with known glaucoma and increased IOP who do not have meaningful vision (light perception only or no light perception) and are not experiencing pain related to the glaucoma, may be eligible after discussion with the study chair. * Subjects with any other significant abnormality on ophthalmic examination should be discussed with the Study Chair for potential eligibility * Ophthalmological findings secondary to long-standing optic pathway glioma (such as visual loss, optic nerve pallor or strabismus) or long-standing orbito-temporal PN (such as visual loss, strabismus) will NOT be considered a significant abnormality for the purposes of the study * Known severe hypersensitivity to selumetinib or any excipient of selumetinib or history of allergic reactions attributed to compounds of similar chemical or biologic composition to selumetinib * Have had recent major surgery within a minimum of 4 weeks prior to starting study treatment, with the exception of surgical placement for vascular access. * Have any unresolved chronic toxicity with CTC AE grade \>= 2, from previous anti-NF1 therapy, except for alopecia. * Clinical judgment by the investigator that the patient should not participate in the study