The employment of single-mode fiber technology, the potentials of coherent optical communication systems, and the novel sensor applications have emphasized the need for integrated optical components, such as couplers, modulators, switches, filters, etc., that are reliable, precise, wavelength selective, and even polarization selective. The design of optimized integrated optical components requires a detailed understanding of the various electromagnetic propagation characteristics of the structures defining the devices. Typical optical structures such as dielectric slab waveguides with junctions, rib waveguides, grating structures, and other dielectric waveguiding geometries could also be made from anisotropic materials, and their properties could be electro-optically altered. In addition to providing optimized design, an accurate method that can simulate the operation of the device allows ways of exploring new concepts. The main objective of this paper is to present the use of these simulation techniques. Three methods for the simulation of the propagation of light through dielectric guiding structures have been considered here. These methods are the finite-difference time-domain (FDTD) method, the coupled-mode theory (CMT) and the beam-propagation method (BPM). The time-explicit FDTD method has been demonstrated to be a very powerful tool in the analysis of arbitrary shaped structures, which may contain abrupt discontinuities in both the propagation and the transverse directions. However, solving an optically long structure by the FDTD method will require a large amount of computer resource. Although the CMT and the BPM are not recommended to analyze a structure with large discontinuities in the propagation direction, they can analyze a long structure very effectively if the transition in the propagation direction is adiabatic. Thus, an optically large (thousands of wavelengths long) structure with bends, junctions, discontinuities, and long guiding structures can be partitioned and solved by a combination of these three techniques. After a review of the various simulation methods for optical circuits, this article focuses on the formulation and the implementation of the FDTD method. Examples are presented on simulations of structures of current practical interest. © 1991.