The multislice algorithm is a method for the simulation of the elastic interaction of an electron beam with matter, including all multiple scattering effects. The method is reviewed in the book by Cowley. The algorithm is used in the simulation of high resolution Transmission electron microscopy micrographs, and serves as a useful tool for analyzing experimental images. Here we describe relevant background information, the theoretical basis of the technique, approximations used, and several software packages that implement this technique. Moreover, we delineate some of the advantages and limitations of the technique and important considerations that need to be taken into account for real-world use. Background The multislice method has found wide application in electron crystallography. The mapping from a crystal structure to its image or diffraction pattern has been relatively well understood and documented. However, the reverse mapping from electron micrograph images to the crystal structure is generally more complicated. The fact that the images are two-dimensional projections of three-dimensional crystal structure makes it tedious to compare these projections to all plausible crystal structures. Hence, the use of numerical techniques in simulating results for different crystal structure is integral to the field of electron microscopy and crystallography. Several software packages exist to simulate electron micrographs. There are two widely used simulation techniques that exist in literature: the Bloch wave method, derived from Hans Bethe's original theoretical treatment of the Davisson-Germer experiment, and the multislice method. In this paper, we will primarily focus on the multislice method for simulation of diffraction patterns, including multiple elastic scattering effects. Most of the packages that exist implement the multislice algorithm along with Fourier analysis to incorporate electron lens aberration effects to determine electron microscope image and address aspects such as phase contrast and diffraction contrast. For electron microscope samples in the form of a thin crystalline slab in the transmission geometry, the aim of these software packages is to provide a map of the crystal potential, however this inversion process is greatly complicated by the presence of multiple elastic scattering. The first description of what is now known as the multislice theory was given in the classic paper by Cowley and Moodie. In this work, the authors describe scattering of electrons using a physical optics approach without invoking quantum mechanical arguments. Many other derivations of these iterative equations have since been given using alternative methods, such as Greens functions, differential equations, scattering matrices or