Smart grid enables the two-way communication between the suppliers and consumers. Price-driven demand response (PDDR) is one of the important demand response categories that uses price of the energy as control signals to affect consumers' electricity consumption. The current PDDR programs include critical peak pricing (CPP), time-of-use (TOU) pricing, and real-time pricing. In this paper, we provide a review of the PDDR studies. Detailed evaluations on advantages and disadvantages of each PDDR are provided. Concerns and future research challenges on PDDR are also addressed. It is believed that with the installation of smart meter infrastructures at residential households, price signal can be an efficient market tool for peak demand shaving, risk and reliability management, carbon emission reduction, and energy cost reduction.