The increasing use of demand-side management as a tool to reliably meet electricity demand at peak time has stimulated interest among researchers, consumers and producer organizations, managers, regulators and policymakers, This research reviews the growing literature on models used to study demand, consumer baseline (CBL) and demand response in the electricity market. After characterizing the general demand models, it reviews consumer baseline based on which further study the demand response models. Given the experience gained from the review and exiting conditions it combines an appropriate model for each case for possible application to the electricity market and discusses the implications of the results. In the literature these aspects are studied independently. The main contribution of this survey is attributed to the simultaneous treatment of the three issues as sequentially interdependent. The review is expected to provide a full understanding of the demand, CBL and demand response in the power market and their relationships. It enhances demand response in the electricity market. The objective is through a combination of demand and supply side managements to reduce demand through different demand response programs during peak times and thereby save costly power generation and energy resources and at the same time reduce vulnerability.