Manual palpation has been used for centuries to provide a relative indication of tissue health and disease. Engineers have sought to make these assessments increasingly quantitative and accessible within daily clinical practice. Since many of the developed techniques involve image-based quantification of tissue deformation in response to an applied force (i.e., "elastography"), such approaches fall squarely within the domain of the radiologist. While commercial elastography analysis software is becoming increasingly available for clinical use, the internal workings of these packages often remain a "black box," with limited guidance on how to usefully apply the methods toward a meaningful diagnosis. The purpose of the present review article is to introduce some important approaches to elastography that have been developed for the most widely used clinical imaging modalities (e.g., ultrasound, MRI), to provide a basic sense of the underlying physical principles, and to discuss both current and potential (musculoskeletal) applications. The article also seeks to provide a perspective on emerging approaches that are rapidly developing in the research laboratory (e.g., optical coherence tomography, fibered confocal microscopy), and which may eventually gain a clinical foothold.