Optical coherence tomography (OCT) has several advantages over other imaging modalities, such as angiography and ultrasound, due to its inherently high in vivo resolution, which allows for the identification of morphological tissue structures. Optical coherence elastography (OCE) benefits from the superior spatial resolution of OCT and has promising applications, including cancer diagnosis and the detailed characterization of arterial wall biomechanics, both of which are based on the elastic properties of the tissue under investigation. We present OCE principles based on techniques associated with static and dynamic tissue excitation, and their corresponding elastogram image-reconstruction algorithms are reviewed. OCE techniques, including the development of intravascular- or catheter-based OCE, are in their early stages of development but show great promise for surgical oncology or intravascular cardiology applications.