Neural quantum states (NQS) are a class of variational states used to simulate quantum many-body systems. Unlike traditional methods that require exponentially many parameters to represent the wave function, NQS use neural networks to compress the state, allowing efficient representation of complex quantum states. This approach overcomes the exponential scaling issue by parameterizing the wave function coefficients through neural network parameters rather than explicitly storing all coefficients. NQS have been applied to simulate ground and excited states, finite temperature states, and open quantum systems, as well as to perform quantum state tomography. They are particularly effective for systems with volume-law entanglement, which are challenging for tensor network methods like matrix product states (MPS). NQS can also be designed for two-dimensional systems and have shown promise in representing a wide range of quantum states. They are used in both simulation and reconstruction tasks, with the ability to efficiently evaluate operators and handle complex quantum dynamics. NQS have been shown to outperform traditional methods in many cases, especially for systems with high entanglement. The review discusses various NQS architectures, including feedforward neural networks, restricted Boltzmann machines, convolutional neural networks, graph neural networks, and transformers, and their applications in quantum simulations. The article also covers the challenges in training NQS, such as non-convex optimization landscapes, and the importance of designing architectures that can capture symmetries and handle different physical systems. Overall, NQS provide a flexible and powerful framework for simulating quantum systems, with ongoing research aimed at improving their performance and applicability.Neural quantum states (NQS) are a class of variational states used to simulate quantum many-body systems. Unlike traditional methods that require exponentially many parameters to represent the wave function, NQS use neural networks to compress the state, allowing efficient representation of complex quantum states. This approach overcomes the exponential scaling issue by parameterizing the wave function coefficients through neural network parameters rather than explicitly storing all coefficients. NQS have been applied to simulate ground and excited states, finite temperature states, and open quantum systems, as well as to perform quantum state tomography. They are particularly effective for systems with volume-law entanglement, which are challenging for tensor network methods like matrix product states (MPS). NQS can also be designed for two-dimensional systems and have shown promise in representing a wide range of quantum states. They are used in both simulation and reconstruction tasks, with the ability to efficiently evaluate operators and handle complex quantum dynamics. NQS have been shown to outperform traditional methods in many cases, especially for systems with high entanglement. The review discusses various NQS architectures, including feedforward neural networks, restricted Boltzmann machines, convolutional neural networks, graph neural networks, and transformers, and their applications in quantum simulations. The article also covers the challenges in training NQS, such as non-convex optimization landscapes, and the importance of designing architectures that can capture symmetries and handle different physical systems. Overall, NQS provide a flexible and powerful framework for simulating quantum systems, with ongoing research aimed at improving their performance and applicability.