The paper provides a comprehensive review of the Long Short-Term Memory (LSTM) model, a powerful recurrent neural network (RNN) designed to address the exploding and vanishing gradient problems. LSTM has transformed machine learning and neurocomputing, improving Google's speech recognition, machine translations on Google Translate, and Amazon's Alexa. The model is also widely used in gaming, such as Google's DeepMind's AlphaStar for playing Starcraft II. The review covers LSTM's formulation, training, and various applications, including text recognition, time series forecasting, natural language processing, computer vision, and image and video captioning. The authors discuss the theoretical foundations of LSTM, its components, and how it interacts with other neural networks. They also present a code example in Tensorflow for predicting the next word in a short story. The review highlights the model's effectiveness in handling long-term dependencies and its ability to capture context and temporal information, making it suitable for a wide range of practical and theoretical applications.The paper provides a comprehensive review of the Long Short-Term Memory (LSTM) model, a powerful recurrent neural network (RNN) designed to address the exploding and vanishing gradient problems. LSTM has transformed machine learning and neurocomputing, improving Google's speech recognition, machine translations on Google Translate, and Amazon's Alexa. The model is also widely used in gaming, such as Google's DeepMind's AlphaStar for playing Starcraft II. The review covers LSTM's formulation, training, and various applications, including text recognition, time series forecasting, natural language processing, computer vision, and image and video captioning. The authors discuss the theoretical foundations of LSTM, its components, and how it interacts with other neural networks. They also present a code example in Tensorflow for predicting the next word in a short story. The review highlights the model's effectiveness in handling long-term dependencies and its ability to capture context and temporal information, making it suitable for a wide range of practical and theoretical applications.