High growth in electricity demand and peaks in the load curve, caused mainly by households, require big investments in infrastructure that are used for short periods. Because of this, it is necessary to look for new developments that allow meeting the needs of users as well as using the electricity system resources efficiently. This is possible through the Smart Grid (SG), which additionally allows users to have autonomy in the electricity supply chain. Our focus of investigation is with households because they can monitor their demand and help to reduce the peaks of the load curve. To do this, users must use Smart Meters, because these devices allow consumers to obtain the information necessary to control their demand. This paper presents a systematic analysis of published literature related to the study of the SG from the demand side, analyses the current situation of this topic and the impact of Smart Meter penetration in households.