A Study of Selpercatinib (LOXO-292) in Participants With Advanced Solid Tumors, RET Fusion-Positive Solid Tumors, and Medullary Thyroid Cancer (LIBRETTO-001)

Key Inclusion Criteria: For Phase 1: * Participants with a locally advanced or metastatic solid tumor that: * Has progressed on or is intolerant to standard therapy, or * For which no standard therapy exists, or in the opinion of the Investigator, are not candidates for or would be unlikely to tolerate or derive significant clinical benefit from standard therapy, or * Decline standard therapy * Prior multikinase inhibitors (MKIs) with anti-RET activity are allowed * A RET gene alteration is not required initially. Once adequate PK exposure is achieved, evidence of RET gene alteration in tumor and/or blood is required as identified through molecular assays, as performed for clinical evaluation * Measurable or non-measurable disease as determined by RECIST 1.1 or RANO as appropriate to tumor type * Eastern Cooperative Oncology Group (ECOG) score of 0, 1, or 2 or Lansky Performance Score (LPS) greater than or equal to (≥) 40 percent (%) (age less than \[\<\] 16 years) with no sudden deterioration 2 weeks prior to the first dose of study treatment * Adequate hematologic, hepatic and renal function * Life expectancy of at least 3 months For Phase 2: As for phase 1 with the following modifications: * For Cohort 1: Participants must have received prior standard therapy appropriate for their tumor type and stage of disease, or in the opinion of the Investigator, would be unlikely to tolerate or derive clinical benefit from appropriate standard of care therapy * Cohorts 1 and 2: * Enrollment will be restricted to participants with evidence of a RET gene alteration in tumor * At least one measurable lesion as defined by RECIST 1.1 or RANO, as appropriate to tumor type and not previously irradiated * Cohorts 3 and 4: Enrollment closed * Cohort 5: * Cohorts 1-4 without measurable disease * MCT not meeting the requirements for Cohorts 3 or 4 * MTC syndrome spectrum cancers (e.g., MTC, pheochromocytoma), cancers with neuroendocrine features/differentiation, or poorly differentiated thyroid cancers with other RET alteration/activation may be allowed with prior Sponsor approval * cfDNA positive for a RET gene alteration not known to be present in a tumor sample * Cohort 6: Participants who otherwise are eligible for Cohorts 1, 2 or 5 who discontinued another RET inhibitor may be eligible with prior Sponsor approval * Cohort 7: Participants with a histologically confirmed stage IB-IIIA NSCLC and a RET fusion; determined to be medically operable and tumor deemed resectable by a thoracic surgical oncologist, without prior systemic treatment for NSCLC Key Exclusion Criteria (Phase 1 and Phase 2): * Phase 2 Cohorts 1 and 2: an additional known oncogenic driver * Cohorts 3 and 4: Enrollment closed * Cohorts 1, 2 and 5: prior treatment with a selective RET inhibitor Notes: Participants otherwise eligible for Cohorts 1, 2, and 5 who discontinued another selective RET inhibitor may be eligible for Phase 2 Cohort 6 with prior Sponsor approval * Investigational agent or anticancer therapy (including chemotherapy, biologic therapy, immunotherapy, anticancer Chinese medicine or other anticancer herbal remedy) within 5 half-lives or 2 weeks (whichever is shorter) prior to planned start of LOXO-292 (selpercatinib). In addition, no concurrent investigational anti-cancer therapy is permitted Note: Potential exception for this exclusion criterion will require a valid scientific justification and approval from the Sponsor * Major surgery (excluding placement of vascular access) within 2 weeks prior to planned start of LOXO-292 (selpercatinib) * Radiotherapy with a limited field of radiation for palliation within 1 week of planned start of LOXO-292 (selpercatinib), with the exception of participants receiving radiation to more than 30% of the bone marrow or with a wide field of radiation, which must be completed at least 4 weeks prior to the first dose of study treatment * Any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 at the time of starting study treatment with the exception of alopecia and Grade 2, prior platinum-therapy related neuropathy * Symptomatic primary CNS tumor, metastases, leptomeningeal carcinomatosis, or untreated spinal cord compression. Participants are eligible if neurological symptoms and CNS imaging are stable and steroid dose is stable for 14 days prior to the first dose of LOXO-292 (selpercatinib) and no CNS surgery or radiation has been performed for 28 days, 14 days if stereotactic radiosurgery (SRS) * Clinically significant active cardiovascular disease or history of myocardial infarction within 6 months prior to planned start of LOXO-292 (selpercatinib) or prolongation of the QT interval corrected (QTcF) greater than (\>) 470 milliseconds (msec) * Participants with implanted pacemakers may enter the study without meeting QTc criteria due to nonevaluable measurement if it is possible to monitor for QT changes. * Participants with bundle branch block may be considered for study entry if QTc is appropriate by a formula other than Fridericia's and if it is possible to monitor for QT changes. * Required treatment with certain strong cytochrome P450 3A4 (CYP3A4) inhibitors or inducers and certain prohibited concomitant medications * Phase 2 Cohort 7 (neoadjuvant treatment): Participant must not have received prior systemic therapy for NSCLC.