Fundamentals of speckle metrology are reviewed, with special emphasis on principles governing speckle formation and dependence of this phenomenon on objects' motion and/or deformation. Processes relating to recording and reconstruction of specklegrams are discussed and are followed by presentation of methods for quantitative interpretation of specklegrams. Solution of the resulting equations, based on the method of projection matrices and the fringe vector theory, is outlined. Applications of speckle metrology techniques to measurement of displacements and strains are presented. Presentation of these applications is illustrated by representative examples from the fields of engineering and medicine, including measurement of displacements and vibrations of objects with diffusely scattering surfaces in real time.