Barrett's esophagus (BE) is a condition that poses high risk of developing dysplasia leading to cancer. Detection of dysplasia is a critical element in determining therapy but is extremely challenging, so that standard white-light endoscopy is used only as a means to guide biopsy. Many novel optical techniques have been aimed at this problem, including various forms of improved wide-field white-light (chromoendscopy/magnification and narrow-band) and fluorescence imaging, and "optical biopsy" techniques (diffuse reflectance, elastic light scattering, fluorescence and Raman spectroscopies, confocal microendoscopy, and optical coherence tomography). While promising, either as stand-alone modalities or in combination, to date none has solved this pivotal challenge to the point of clinical adoption. Likewise, minimally invasive treatment of BE patients with dysplasia remains suboptimal, despite recent approval of photodynamic therapy for this indication. This work presents a critique and summary of each of these biophotonic technologies, and discusses the fundamental advantages and limitations of each. The future directions for this field are considered, particularly from the perspective of relying on intrinsic (endogenous) optical signatures compared with the use of exogenous contrast agents.