The integration of renewable energy sources, such as solar and wind power, into power grids has become crucial for addressing environmental concerns and achieving sustainable energy goals. However, the inherent variability and intermittency of these energy sources pose significant challenges for grid management. To address this, accurate forecasting of power generation has garnered increasing interest, leading to the adoption of machine learning techniques. Among these techniques, networks with long short-term memory (LSTM) and artificial neural networks (ANN) have emerged as promising solutions for time series forecasting due to their ability to capture temporal dependencies and non-linear patterns. This review provides a comprehensive examination of the existing three architectures used for power generation prediction. The review begins by introducing the foundational concepts of ANN and LSTMs, and then it delves into various applications of this method in power generation forecasting. The reviewed studies are categorized based on the dataset used, the model, and a summary of the work configurations. Finally, this review contributes to a deeper understanding of existing ANN-LSTM architectures and paves the way for enhanced forecasting models, thus promoting a sustainable energy future.