This review describes the unique opportunities and challenges for noninvasive optical mapping of human brain function. Diffuse optical methods offer safe, portable, and radiation free alternatives to traditional technologies like positron emission tomography or functional magnetic resonance imaging (fMRI). Recent developments in high-density diffuse optical tomography (HD-DOT) have demonstrated capabilities for mapping human cortical brain function over an extended field of view with image quality approaching that of fMRI. In this review, we cover fundamental principles of the diffusion of near infrared light in biological tissue. We discuss the challenges involved in the HD-DOT system design and implementation that must be overcome to acquire the signal-to-noise necessary to measure and locate brain function at the depth of the cortex. We discuss strategies for validation of the sensitivity, specificity, and reliability of HD-DOT acquired maps of cortical brain function. We then provide a brief overview of some clinical applications of HD-DOT. Though diffuse optical measurements of neurophysiology have existed for several decades, tremendous opportunity remains to advance optical imaging of brain function to address a crucial niche in basic and clinical neuroscience: that of bedside and minimally constrained high fidelity imaging of brain function.