In the present paper we review the state of the art of two complementary propagation techniques with applications for integrated optics device modeling: The Finite-Difference Time-Domain and the Beam Propagation Method. In both cases we focus on their main features such as the types of propagation schemes and the material effects that can be modeled. In addition, we also consider a 2D mode solver based on a complex root finding procedure-a representative mode solving technique that is of significant interest for design and modeling of leaky mode based devices. Each of the methods is illustrated with appropriate simulation examples of devices and waveguide structures being of current research interest: photonic band gap structures, waveguide gratings, ARROW waveguides etc. The selected examples show the power of the methods as well as the consistency and the complementarity of their results when applied together.