Massive MIMO (multiple‐input multiple‐output) is a fundamental technology in 5G systems. The characteristics of the radio channel experienced when operating with large antenna arrays differ from those of conventional multiple antenna systems. Hence, it is important to specifically characterize and model the underlying propagation channels with large antenna systems in mind. The channel models need to be realistic and accurate, but of low complexity, in order to be used to develop and assess the performance of future systems in a good way. This article gives an overview of state‐of‐the‐art of massive MIMO channels and related models. First, some fundamentals of massive MIMO propagation, including a comparison between micro‐wave and mm‐wave massive MIMO as well as the influence of user terminals, are provided. Then, channel characteristics that have been shown in measurements to be important in massive MIMO channels are presented. These include spherical wavefronts, nonstationarity, 3D propagation, and polarization effects. Further on, some channel‐dependent characteristics, which are experienced in massive MIMO systems, are in focus. In this article, we outline user separability and channel hardening, as an effect of favorable propagation conditions. Different channel modeling approaches are discussed, including the independent and identically distributed (i.i.d.) complex Gaussian channel model, correlation‐based channel models like the Kronecker and Weichselberger channel models, geometry‐based reference models, geometry‐based stochastic channel models (GSCMs), ray‐tracing and map‐based approaches. A brief overview of recently developed channel models, targeting massive MIMO channels, is also provided. Lastly, we discuss opportunities and challenges related to massive MIMO channels and modeling.