The integration of combined heat and power (CHP) systems, coupled with intelligent control methods, have a considerable effect in enhancing energy efficiency and sustainability by concurrently producing electricity and useful thermal energy. In this regard, a comprehensive review over these intelligent methodologies can be a considerable resource. Consequently, the proposed review comprehensively explores the significance of CHP systems, focusing on their prevalence in the USA and Europe, backed by statistical insights. The mathematical foundations of CHP systems are presented, setting the stage for an in-depth analysis of advancements and intelligent control methods in optimal planning, economic dispatch, and cost minimization goals in CHP system. Intelligent models, including long short-term memory (LSTM), Bi-directional LSTM (BiLSTM), and Random Forest, are mathematically described and subsequently applied to a simulated CHP system. Key Performance Indicators (KPIs) derived from these models demonstrate their potential efficacy in efficiently controlling CHP systems. Finally, the findings present the effect of intelligent artificial intelligence (AI)-driven models, such as LSTM, BiLSTM, and Random Forest, in optimizing CHP system performance. Looking ahead perspectives, the paper envisions CHP systems as fundamental elements in the futuristic modern power sustainable energy efficient systems.