This review article provides an overview of neural quantum states (NQS), a relatively new class of variational states designed to simulate quantum many-body systems. NQS overcome the exponential scaling of Hilbert space dimension by compressing the state into network parameters rather than storing all coefficients. The article introduces common NQS architectures and their applications in simulating ground and excited states, finite temperature states, open system states, and dynamics. It also discusses NQS in the context of quantum state tomography. NQS have been shown to represent volume-law entangled states, making them suitable for a broad range of quantum systems, including two-dimensional problems and fermionic systems. The review covers various NQS architectures, such as feedforward neural networks (FFNNs), restricted Boltzmann machines (RBMs), convolutional neural networks (CNNs), graph neural networks (GNNs), autoregressive networks, recurrent neural networks (RNNs), and transformers. Each architecture is discussed in terms of its advantages, disadvantages, and specific applications. The article highlights the potential of NQS in overcoming challenges in quantum state simulation, such as the sign problem and slow convergence in quantum Monte Carlo methods. The review concludes with a summary of the current state of NQS and their performance compared to conventional methods.This review article provides an overview of neural quantum states (NQS), a relatively new class of variational states designed to simulate quantum many-body systems. NQS overcome the exponential scaling of Hilbert space dimension by compressing the state into network parameters rather than storing all coefficients. The article introduces common NQS architectures and their applications in simulating ground and excited states, finite temperature states, open system states, and dynamics. It also discusses NQS in the context of quantum state tomography. NQS have been shown to represent volume-law entangled states, making them suitable for a broad range of quantum systems, including two-dimensional problems and fermionic systems. The review covers various NQS architectures, such as feedforward neural networks (FFNNs), restricted Boltzmann machines (RBMs), convolutional neural networks (CNNs), graph neural networks (GNNs), autoregressive networks, recurrent neural networks (RNNs), and transformers. Each architecture is discussed in terms of its advantages, disadvantages, and specific applications. The article highlights the potential of NQS in overcoming challenges in quantum state simulation, such as the sign problem and slow convergence in quantum Monte Carlo methods. The review concludes with a summary of the current state of NQS and their performance compared to conventional methods.