The ability to control and optimise energy consumption at end-user level is of increasing interest as a means to achieve a balance between supply and demand, particularly when large penetration of distributed renewable energy sources is being considered. Demand Response programs consist of a series of externally-driven control strategies aimed at adapting consumer end-use load to specific grid requirements. In a demand response scenario, a network of connected systems can be exploited to activate balancing strategies, to provide demand flexibility during periods of high stress for the grid. However, the widespread deployment of demand response programs in the building sector still faces significant challenges. Smart technology deployment, the lack of common standardised assessment procedures and metrics, the absence of established regulatory frameworks are among the main obstacles limiting the development of portfolios of competitive flexibility assets. The residential sector is even more affected by these challenges due to a marginal economic case, the issue of long term harmonisation of hardware and software infrastructure and the influence of the end-user behaviour and preferences on energy consumption. The present paper provides a review on the current developments of the Demand Response programs, with specific reference to the residential building sector. Methodologies and procedures for assessing building energy flexibility and Demand Response programs are described with a special focus on numerical models and available control algorithms. Moreover, markets schemes and social aspects - such as technology acceptance and awareness - and their influence on smart control technologies and algorithms are discussed. Current research gaps and challenges are identified and analysed to provide guidance for future research activities.