Forecasting electricity load demand is critical for power system planning and energy management. In particular, accurate short-term load forecasting (STLF), which focuses on the lead time horizon of few minutes to one week ahead, can help in better load scheduling, unit commitment, and cost-effective operation of smart power grids. In the last decade, different artificial intelligence (AI)-based techniques and metaheuristic algorithms have been utilized for STLF by the researchers and scientists with varying degrees of accuracy and efficacy. Despite the benefits of implemented methods for STLF, many drawbacks and associated problems have also been observed and reported by the researchers. This paper provides a comprehensive review of hybrid deep learning models based on nature-inspired metaheuristic techniques for STLF with respect to the analysis of the results and accuracy. Moreover, it also provides the research findings and gaps that will assist the researchers to have an early awareness of all important benefits and drawbacks of these integrated STLF methods scientifically and systematically. Especially, the hybrid forecast models using artificial intelligence-based methods for smart grids are focused. Several performance indices are used to compare and report the accuracy of these techniques including mean absolute percentage error (MAPE). Multiple other parametric and exogenous variable details have also been focused to figure out the potential of the intelligent load forecasting techniques from the perspective of smart power grids.