When light is incident to a biological tissue surface, combinations of optical processes occur, such as reflection, absorption, elastic and non-elastic scattering, and fluorescence. Analysis of these light interactions with the tissue provides insight into the metabolic and pathological state of the tissue. Furthermore, in vivo diagnosis of diseases using optical spectroscopy enables in situ rapid clinical decisions without invasive biopsies. For in vivo scenarios, incident light can be delivered in a highly localized manner to tissue via optical fibers, which are placed within the working channels of minimally invasive clinical tools, such as endoscopes. There has been extensive development in the accuracy and specificity of these optical spectroscopy techniques since the earliest in vivo examples were published in the academic literature in the early '90s, and there are now commercially available systems that have undergone medical and clinical trials. In this review, several types of optical spectroscopy techniques (elastic optical scattering spectroscopy, fluorescence spectroscopy, Raman spectroscopy, and multimodal spectroscopy) for the diagnosis and monitoring of diseases states of tissue in an in vivo setting are introduced and explored. Examples of the latest and most impactful works for each technique are then critically reviewed. Finally, current challenges and unmet clinical needs are discussed, followed by future opportunities, such as point-based spectroscopies for robot-guided surgical interventions.