Full-field displacement and strain measurements of materials, structures and biological tissues subjected to various external (i.e. mechanical or thermal) loading is a primary task of experimental solid mechanics. For nearly a century, benefiting from the rapid development of different branches of physics, various new techniques for whole-field displacement and strain measurements have been developed, advocated and widely used. However, most of these techniques only allows for surface deformation measurement, while in most cases the surface deformation is very different from the actual deformation throughout the interior of a test object. To quantify full-field internal 3D deformation of various opaque materials or biologic tissues subjected to external loading, digital volume correlation (DVC) was developed at the end of last century. Thanks to the increasing popularity and constant emergence of various volumetric imaging devices (e.g., X-ray computed tomography), internal microstructure of a tested sample arising from natural texture or embedded particles can be recorded as digital volume image with distinct random grayscale distribution. By comparing the volume images recorded at different configurations, the internal kinematic filed of the sample can be accurately retrieved by DVC algorithm with the assistance of advanced 3D image registration algorithms and modern computational facilities. Benefiting from constant emergence of new 3D imaging facilities, continual refinement of image registration algorithms, and rapid development of high-performance parallel computing technologies, DVC has gained numerous successful applications in biomedicine, solid mechanics, rock and geo mechanics, material science and biomedicines etc. Basically, as an image-based experimental technique, the implementation of DVC for internal deformation measurement comprises two consecutive steps: volume image acquisition using a certain 3D imaging device and image processing using 3D image registration algorithm. Thus, the accuracy and precision of DVC measurements depend on two primary components: the quality of the recorded volumetric images and the performance of DVC algorithms. In order to satisfy the increasing requirement of measurement accuracy in practical applications, many researchers have contributed to investigate the algorithm improvement and imaging error calibration. In the past decade, plenty of methodologies and algorithmic details have been developed to realize higher measurement accuracy and computational efficiency. Although both the image quality and algorithm performance have gain significant improvement in recent years, systematic and random errors inevitably occur during DVC analyses due to the influence of internal microstructure, image acquirement system, loading environment and algorithm details, thus posing important challenge to accurate DVC measurement in practical applications. In this review, the basic principles and procedures of DVC approach and the concept of the algorithmic details are briefly described first. Then, various methodologies and algorithmic details employed in DVC for internal 3D displacement and strain measurement are systematically described and commented. Limitations and potential developments of the technique are also summarized in terms of material microstructure, volumetric imaging and algorithm performance. Despite facing several challenges such as highly dependence on internal microstructure and large data processing with relatively lower computational efficiency, it is foreseen that DVC method will play an increasingly important role in the field of experimental mechanics and definitely expect more potential applications in broad areas especially in material science and biological engineering.