Cancer is a complex disease in which both genetic defects and microenvironmental components contribute to the development, progression, and metastasization of disease, representing major hurdles in the identification of more effective and safer treatment regimens for patients. Three-dimensional (3D) models are changing the paradigm of preclinical cancer research as they more closely resemble the complex tissue environment and architecture found in clinical tumors than in bidimensional (2D) cell cultures. Among 3D models, spheroids and organoids represent the most versatile and promising models in that they are capable of recapitulating the heterogeneity and pathophysiology of human cancers and of filling the gap between conventional 2D in vitro testing and animal models. Such 3D systems represent a powerful tool for studying cancer biology, enabling us to model the dynamic evolution of neoplastic disease from the early stages to metastatic dissemination and the interactions with the microenvironment. Spheroids and organoids have recently been used in the field of drug discovery and personalized medicine. The combined use of 3D models could potentially improve the robustness and reliability of preclinical research data, reducing the need for animal testing and favoring their transition to clinical practice. In this review, we summarize the recent advances in the use of these 3D systems for cancer modeling, focusing on their innovative translational applications, looking at future challenges, and comparing them with most widely used animal models.