One of the promising directions in personalized medicine is the use of three-dimensional (3D) tumor models such as spheroids and organoids. Spheroids and organoids are three-dimensional cultures of tumor cells that can be obtained from patient tissue and, using high-throughput personalized medicine methods, provide a suitable therapy for that patient. These 3D models can be obtained from most types of tumors, which provides opportunities for the creation of biobanks with appropriate patient materials that can be used to screen drugs and facilitate the development of therapeutic agents. It should be noted that the use of spheroids and organoids would expand the understanding of tumor biology and its microenvironment, help develop new in vitro platforms for drug testing and create new therapeutic strategies. In this review, we discuss 3D tumor spheroid and organoid models, their advantages and disadvantages, and evaluate their promising use in personalized medicine.