In recent years extensive research has been conducted on the development of different models that enable energy trading between prosumers and consumers due to expected high integration of distributed energy resources. Some of the most researched mechanisms include Peer-to-Peer energy trading, Community Self-Consumption and Transactive Energy Models. To ensure the stable and reliable delivery of electricity as such markets and models grow, this paper aims to understand the impact of these models on grid infrastructure, including impacts on the control, operation, and planning of power systems, interaction between multiple market models and impact on transmission network. Here, we present a comprehensive review of existing research on impact of Local Energy Market integration in power systems layer. We detect and classify most common issues and benefits that the power grid can expect from integrating these models. We also present a detailed overview of methods that are used to integrate physical network constraints into the market mechanisms, their advantages, drawbacks, and scaling potential. In addition, we present different methods to calculate and allocate network tariffs and power losses. We find that financial energy transactions do not directly reflect the physical energy flows imposed by the constraints of the installed electrical infrastructure. In the end, we identify a number of different challenges and detect research gaps that need to be addressed in order to integrate Local Energy Market models into existing infrastructure.