Spheroids and organoids are important novel players in medical and life science research. They are gradually replacing two-dimensional (2D) cell cultures. Indeed, three-dimensional (3D) cultures are closer to the in vivo reality and open promising perspectives for academic research, drug screening, and personalized medicine. A large variety of cells and tissues, including tumor cells, can be the starting material for the generation of 3D cultures, including primary tissues, stem cells, or cell lines. A panoply of methods has been developed to generate 3D structures, including spontaneous or forced cell aggregation, air-liquid interface conditions, low cell attachment supports, magnetic levitation, and scaffold-based technologies. The choice of the most appropriate method depends on (i) the origin of the tissue, (ii) the presence or absence of a disease, and (iii) the intended application. This review summarizes methods and approaches for the generation of cancer spheroids and organoids, including their advantages and limitations. We also highlight some of the challenges and unresolved issues in the field of cancer spheroids and organoids, and discuss possible therapeutic applications.