Conventional computed tomography (CT) remains the workhorse of cross-sectional medical imaging. But dual- and multi-energy CT allows for more specific material decomposition, enabling distinct advantages in the clinical setting. In this review, we describe the basic principles behind material decomposition in dual- and multi-energy CT, outline the techniques used to acquire images, and explore how enhanced material decomposition leads to improved patient care. We also explore areas of active research and future directions, including photon-counting CT, that have the potential to revolutionize CT in clinical use.