(Received ?; revised ?; accepted ?. -To be entered by editorial office)Firstly, a brief overview will be given on different models that are able to describe the behaviour of wave propagation as a function of specific frequency ranges. Each range corresponds to different heating systems, namely, 20-100 MHz for the Ion Cyclotron Resonant Heating (ICRH), 2-20 GHz for Lower Hybrid Heating or Current Drive (LHCD), and 100-250 GHz for Electron Cyclotron Resonant Heating (ERCH) or Current Drive (ECCD) systems. Every systems' specifications will be explained in detail, including the typical set of equations and the assumptions needed to describe the properties of these heating or current drive systems, as well as their specific domains of validity. In these descriptions, special attention will be paid to the boundary conditions. A review about specific physical problems associated with the wave heating systems will also be provided. Such review will detail the role of simulation in answering questions coming from experiments on magnetized plasma devices devoted to Fusion. A few examples which will be covered are the impact of edge turbulence on wave propagation and its consequences on the heating system performances, effects of the fast particles, ponderomotive effects, among others. A study that is more focused on Radio Frequency (RF) sheath effects will also be discussed. It shows that such simulations require very sophisticated tools to gain a partial understanding of the observations undertaken in dedicated experiments. To conclude this review, an overview will be given about the requirements and progress necessary to obtain relevant predictive simulation tools able to describe the wave heating systems used in fusion devices.