Hopfield Neural Networks (HNNs) are a classical form of recurrent neural networks designed for associative memory, optimization, and pattern completion tasks. They consist of fully connected neurons with symmetric weights, where the network dynamics converge to stable states representing stored patterns. Early research focused on binary Hopfield networks for memory retrieval and solving combinatorial optimization problems such as the traveling salesman problem. Subsequent advancements extended HNNs to continuous-valued neurons, stochastic Hopfield networks, and modern variants integrated with deep learning for energy-based modeling and constrained optimization. Applications span pattern recognition, image restoration, optimization, neural associative memory, and combinatorial problem solving. Recent research explores connections with modern architectures, including attention mechanisms, graph neural networks, and modern energy-based models, as well as hardware implementations for efficient memory retrieval. These developments position Hopfield networks as a foundational paradigm for understanding recurrent dynamics, associative memory, and energy-based neural computation in both classical and contemporary machine learning contexts.