Quantitative magnetic resonance imaging (MRI) techniques have the ability to quantitatively report various pathophysiological processes associated with cancer. These measures have been shown to provide complementary information to that typically obtained from standard morphologically based criteria (e.g., size) and, furthermore, have been shown to outperform sized based measures in certain applications. In this review, we discuss eight areas of quantitative MRI that are either currently employed in clinical trials, or are emerging as promising techniques for both diagnosing cancer as well as assessing—or even predicting—the response of cancer to various therapies. The currently employed methods include the response evaluation criteria in solid tumors (RECIST), dynamic susceptibility MRI (DSC-MRI), dynamic contrast enhanced MRI (DCE-MRI), and diffusion weighted imaging (DWI). The emerging techniques covered are chemical exchange saturation transfer MRI (CEST-MRI), elastography, hyperpolarized MRI, and multi-parameter MRI. After a brief introduction to each technique, we present a small number of illustrative applications before noting the existing limitations of each method and what must be done to move each to more routine clinical application.