The increasing data traffic rate of wire-less communication systems forces the development of new technologies mandatory. Providing high data rate, extremely low latency and improvement on qual-ity of service are the main subjects of next generation 5G wireless communication systems which will be in the people's life in the years of 2020. As the newest and first mathematically proven forward error correc-tion code, polar code is one of the best candidates among error correction methods that can be employed for 5G wireless networks. The aim of this tutorial is to show that belief propagation decoding of polar codes can be a promising forward error correction technique in upcoming 5G frameworks. First, we survey the novel approaches to the belief propagation based de-coding of polar codes and continue with the studies about the simplification of these decoders. Moreover, early detection and termination methods and concept of scheduling are going to be presented throughout the manuscript. Finally, polar construction algorithms, error types in belief propagation based decoders and hardware implementations are going to be mentioned. Overall, this tutorial proves that the BP based decod-ing of polar codes has a great potential to be a part of communication standards.