There is no doubt that BitTorrent nowadays is one of the most popular peer-to-peer (P2P) applications on the Internet, contributing to a significant portion of the total Internet traffic and being a basis for many other emerging services such as P2P Internet Protocol Television and Video on Demand. On the other hand, Network Address Translation (NAT) devices have become pervasive in almost all networking scenarios. Despite of the effort of NAT traversal, it is still very likely that applications, especially P2P ones, cannot receive incoming connection requests properly if they are behind NAT. Although this phenomenon has been widely observed in measurement work, so far there is no quantitative study in the literature examining the impact of NAT on P2P applications. In this work, we build analytical models to capture the performance of BitTorrent-like P2P systems in a steady state, in the presence of homogeneous and heterogeneous NAT peers. We also propose biased optimistic unchoke strategies, in order to improve the overall system performance and fairness metrics considerably. The analytical models have been validated by simulation results, which also reveal some interesting facts about the coexistence of NAT and public peers in P2P systems.