The Internet has become a vital information infrastructure for modern society. However, the concurrent nature of network introduces a wide-range of difficulties in traditional programming methodology in developing high-quality network programs that significantly reduce productivity. The influence of concurrency on the complexity of software development is comparable to the “concurrency crisis” of software brought by multi-core processors, but it receives much less attention here than what it deserves. There is no universal approach to cope with this issue, and there are even disagreements between different approaches. In this paper, the basic concurrency models and their implementations are introduced, and then the paper surveys the inherent complexities of these approaches, comparing their advantages and disadvantages. Finally, this paper offers an opinion on the possibilities for future research on this topic.