Smart grid (SG) is a next-generation grid which is responsible for changing the lifestyle of modern society. It avoids the shortcomings of traditional grids by incorporating new technologies in the existing grids. In this paper, we have presented SG in detail with its features, advantages, and architecture. The demand side management techniques used in smart grid are also presented. With the wide usage of domestic appliances in homes, the residential users need to optimize the appliance scheduling strategies. These strategies require the consumer’s flexibility and awareness. Optimization of the power demand for home appliances is a challenge faced by both utility and consumers, particularly during peak hours when the consumption of electricity is on the higher side. Therefore, utility companies have introduced various time-varying incentives and dynamic pricing schemes that provides different rates of electricity at different times depending on consumption. The residential appliance scheduling problem (RASP) is the problem of scheduling appliances at appropriate periods considering the pricing schemes. The objectives of RASP are to minimize electricity cost (EC) of users, minimize the peak-to-average ratio (PAR), and improve the user satisfaction (US) level by minimizing waiting times for the appliances. Various methods have been studied for energy management in residential sectors which encourage the users to schedule their appliances efficiently. This paper aims to give an overview of optimization techniques for residential appliance scheduling. The reviewed studies are classified into classical techniques, heuristic approaches, and meta-heuristic algorithms. Based on this overview, the future research directions are proposed.