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From the earliest beginnings of mobile communications to the present time, there has always been a high demand for realistic mobile radio channel models. This demand is driven by the fact that channel models are indispensable for the performance evaluation, parameter optimisation, and test of mobile communication systems. Channel modelling and simulation techniques are therefore of great importance for electronics and telecommunication engineers who are involved in the development of present and future mobile communication systems. This presentation will start with a review of the basic principles of mobile radio channel modelling and gradually moves to more advanced modelling and simulation techniques. The objective is to provide an overview on commonly used design methodologies enabling the development of channel models for present and future wireless communication systems. All presented channel models have in common that they are derived from a superposition of a finite number of complex sinusoids. However, the design methodologies differ in the way of computing the model parameters determining the statistical behaviour of the channel model. It will be shown that the proposed channel models are widely flexible, which enables an excellent fitting of their principal statistical properties against measurement data of real-world channels or against the statistics of specified reference channel models. Special interest will be paid to the presentation of cutting-edge research on the modelling of mobile-to-mobile MIMO channels, vehicle-to-vehicle MIMO channels, and mobile channels for relay-based cooperative networks. In addition, techniques will be presented for the development of measurement-based mobile radio channel models. The statistical properties of the channel models will be investigated with emphasis on the distribution of the received envelope as well as with respect to the channels' correlation properties in the space, time, and frequency domains. The obt- ined results show that the statistical properties of the channel models required for future mobile communication systems are quite different from the statistics of the channel models used in present mobile communication systems. The presentation closes with a discussion of open research problems in the area.