A Study of Selpercatinib (LY3527723) in Participants With Advanced Solid Tumors Including RET Fusion-positive Solid Tumors, Medullary Thyroid Cancer and Other Tumors With RET Activation

Inclusion Criteria: * Participants with a locally advanced or metastatic solid tumor. * Evidence of a RET gene alteration in tumor and/or blood. * Measurable or non-measurable disease as determined by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1. * Eastern Cooperative Oncology Group (ECOG) performance status score of 0, 1, or 2, with no sudden deterioration 2 weeks prior to the first dose of study treatment. * Archived tumor tissue sample available for cohort 1 and 2. * Cohorts 1 and 2: failed or intolerant to standard of care. * Cohorts 1-2: enrollment will be restricted to participants with evidence of a RET gene alteration in tumor (i.e., not just blood). However, a positive germline DNA test for a RET gene mutation as defined in the protocol is acceptable in the absence of tumor tissue testing for participants with MTC. * Cohorts 1-2: at least one measurable lesion as defined by RECIST v1.1 and not previously irradiated (unless progressive disease for the irradiated lesion\[s\] has been radiographically documented). Exclusion Criteria: * Cohorts 1-2, an additional validated oncogenic driver that could cause resistance to selpercatinib treatment if known. * Prior treatment with a selective RET inhibitor(s) (including investigational selective RET inhibitor(s), such as BLU-667, RXDX-105, etc). * Are currently enrolled in any other clinical study involving an investigational product or any other type of medical research judged not to be scientifically or medically compatible with this study. * Any unresolved toxicities from prior therapy greater than common terminology criteria for adverse events (CTCAE) Grade 1 except where otherwise noted in this eligibility criteria at the time of starting study treatment with the exception of alopecia and Grade 2, prior platinum therapy-related neuropathy. * Symptomatic primary central nervous system (CNS) tumor, symptomatic CNS metastasis, leptomeningeal carcinomatosis, or untreated spinal cord compression. * Clinically significant active cardiovascular disease or history of myocardial infarction within 6 months prior to planned start of selpercatinib or prolongation of the QT interval corrected for heart rate using Fridericia's formula (QTcF) \> 470 milliseconds. * History of Human Immunodeficiency Virus (known HIV 1/2 antibodies positive); participants with unknown HIV status do not need to be tested. * History of active hepatitis B (known positive hepatitis B surface antigen \[HbsAg\] and quantitative hepatitis B DNA greater than the upper limit of detection of the assay) or C (known positive hepatitis C antibody and quantitative hepatitis C RNA greater than the upper limit of detection of the assay); participants with unknown hepatitis B/hepatitis C status do not need to be tested. * Active uncontrolled systemic bacterial, viral, or fungal infection or serious ongoing intercurrent illness, such as hypertension or diabetes, despite optimal treatment. Screening for chronic conditions is not required. * Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal absorption of the study drug. * Uncontrolled symptomatic hyperthyroidism or hypothyroidism * Uncontrolled symptomatic hypercalcemia or hypocalcemia. * Concurrent use of drugs known to prolong QTc. * Pregnancy or lactation. Breast-feeding should be interrupted when selpercatinib is started; breast-feeding can be resumed 3 months after discontinuation of selpercatinib. * Active second malignancy other than minor treatment of indolent cancers with prior sponsor approval.