Optimizing the power demand for smart home appliances in a smart grid is the primary challenge faced by power supplier companies, particularly during peak periods, due to its considerable effect on the stability of a power system. Therefore, power supplier companies have introduced dynamic pricing schemes that provide different prices for a time horizon in which electricity prices are higher during peak periods due to the high power demand and lower during off-peak periods. The problem of scheduling smart home appliances at appropriate periods in a predefined time horizon in accordance with a dynamic pricing scheme is called power scheduling problem in a smart home (PSPSH). The primary objectives in addressing PSPSH are to reduce the electricity bill of users and maintain the stability of a power system by reducing the ratio of the highest power demand to the average power demand, known as the peak-to-average ratio, and to improve user comfort level by reducing the waiting time for appliances. In this paper, we review the most pertinent studies on optimization methods that address PSPSH. The reviewed studies are classified into exact algorithms and metaheuristic algorithms. The latter is categorized into single-based, population-based, and hybrid metaheuristic algorithms. Accordingly, a critical analysis of state-of-the-art methods are provided and possible future directions are also discussed.