The use of three‐dimensional (3D) culture models for cancer research has expanded greatly in recent years, with studies in almost every tumor type addressing a wide variety of research questions. Multiple distinct 3D culture approaches are now available, each with its own advantages and disadvantages, as well as most effective applications. In this review, we focus on one of these 3D culture models, organoids, in which multicellular units are isolated from primary or metastatic tumors and cultured in extracellular matrix gels. Organoids can be studied in acute cultures for short times after isolation, or passaged and biobanked for long‐term use. We define this model system and describe some key studies in which organoid culture models were used to investigate cellular strategies and molecular mechanisms driving cancer initiation and progression, highlighting research questions for which this model is particularly well suited. In addition, as interest in implementing organoid systems continues to expand, we discuss key considerations in developing a new organoid research program. Our goal is to demonstrate the power and utility of organoid models and provide guidance for investigators who are considering implementation of these models in their own research programs. © 2021 The Pathological Society of Great Britain and Ireland. Published by John Wiley & Sons, Ltd.