Polarization is a fundamental property of light and a powerful sensing tool that has been applied to many areas. A Mueller matrix is a complete mathematical description of the polarization characteristics of objects that interact with light, and is known as a transfer function of Stokes vectors which characterise the state of polarization of light. Mueller polarimetric imaging measures Mueller matrices over a field of view and thus allows for visualising the polarization characteristics of the objects. It has emerged as a promising technique in recent years for tissue imaging, improving image contrast and providing a unique perspective to reveal additional information that cannot be resolved by other optical imaging modalities. This review introduces the basis of the Stokes-Mueller formulism, interpretation methods of Mueller matrices into fundamental polarization properties, polarization properties of biological tissues, and considerations in the construction of Mueller polarimetric imaging devices for surgical and diagnostic applications, including primary configurations, optimization procedures, calibration methods as well as the instrument polarization properties of several widelyused biomedical optical devices. The paper also reviews recent progress in Mueller polarimetric endoscopes and fibre Mueller polarimeters, followed by the future outlook in applying the technique to surgery and diagnostics. Tissue polarization properties convey morphological, micro-structural and compositional information of tissue with great potential for label free characterization of tissue pathological changes. Recent progress in tissue polarimetric imaging and polarization resolved endoscopy paved the way for translation of polarimetric imaging to surgery and tissue diagnosis.