Demand Response (DR) in residential sector is considered to play a key role in the smart grid framework because of its disproportionate amount of peak energy use and massive integration of distributed local renewable energy generation in conjunction with battery storage devices. In this paper, first a quick overview about residential demand response and its optimization model at single home and multi-home level is presented. Then a description of state-of-the-art optimization methods addressing different aspects of residential DR algorithms such as optimization of schedules for local RE based generation dispatch, battery storage utilization and appliances consumption by considering both cost and comfort, parameters uncertainty modeling, physical based dynamic consumption modeling of various appliances power consumption at single home and aggregated homes/community level are presented. The key issues along with their challenges and opportunities for residential demand response implementation and further research directions are highlighted.