This chapter focuses on the computational aspects of moments of digital images. In digital image processing, all quantities have to be converted from the continuous to the discrete domain, and efficient algorithms for dealing with discrete quantities must be developed. The chapter shows how the definition of image moments can be converted from the continuous domain to the discrete one. The methods for fast computation of the moments of binary images can be divided into two groups referred to as the boundary-based methods and the decomposition methods. A majority of the boundary-based methods use the Green's theorem, which evaluates the double integral over the object by means of line integration along the object boundary. The decomposition algorithms are more time-consuming. Decomposition into rectangular blocks can only be applied to the objects in volumetric representation. Approximation methods are algorithms for computation of moments of graylevel images that reach low complexity at the expense of accuracy.