A brief summary of the effect of router buffers on network performance is presented. The previous buffer sizing works based on queuing theory are analyzed under two classes of traffic models, the models exhibiting long-range dependence and the models exhibiting short-range dependence. Another type of buffer sizing works are based on TCP models, and the rule of thumb, the small buffers rule, the drop-based buffers rule and the tiny buffers rule are the four main recent results in these works. The results of the four rules and some preliminary experiments to validate these rules are carefully summarized. Research directions and open problems are also discussed.