Tumors are unique and complex ecosystems, in which heterogeneous cell subpopulations with variable molecular profiles, aggressiveness, and proliferation potential coexist and interact. Understanding how heterogeneity influences tumor progression has important clinical implications for improving diagnosis, prognosis, and treatment response prediction. Several recent innovations in data acquisition methods and computational metrics have enabled the quantification of spatiotemporal heterogeneity across different scales of tumor organization. Here, we summarize the most promising efforts from a common experimental and computational perspective, discussing their advantages, shortcomings, and challenges. With personalized medicine entering a new era of unprecedented opportunities, our vision is that of future workflows integrating across modalities, scales, and dimensions to capture intricate aspects of the tumor ecosystem and to open new avenues for improved patient care.