Medulloblastoma (MB) is a highly malignant cerebellar tumor predominantly diagnosed during childhood. Driven by pathogenic activation of sonic hedgehog (SHH) signaling, SHH subgroup MB (SHH-MB) accounts for nearly one-third of diagnoses. Extensive molecular analyses have identified biologically and clinically relevant intertumoral heterogeneity among SHH-MB tumors, prompting the recognition of novel subtypes. Beyond germline and somatic mutations promoting constitutive SHH signaling, driver alterations affect a multitude of pathways and molecular processes, including TP53 signaling, chromatin modulation, and post-transcriptional gene regulation. Here, we review recent advances in the underpinnings of SHH-MB in the context of molecular subtypes, clarify novel somatic and germline drivers, highlight cellular origins and developmental hierarchies, and describe the composition of the tumor microenvironment and its putative role in tumorigenesis.