The article provides a comprehensive overview of quantum simulation, a method to study quantum systems by using other controllable quantum systems. Quantum simulation is particularly useful for systems with large numbers of particles, where classical computers struggle due to the exponential growth in computational complexity. The authors discuss the challenges and potential applications of quantum simulation in various fields such as condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation can be implemented in two main ways: digital quantum simulation (DQS) and analog quantum simulation (AQS). DQS involves encoding the wavefunction of the system into a quantum register and performing unitary transformations to simulate the system's evolution. AQS, on the other hand, uses a controllable quantum system that mimics the dynamics of another quantum system. Both methods have their advantages and limitations, and the choice between them depends on the specific problem and the capabilities of the simulator. The article also covers resource estimation, which is crucial for determining the feasibility of quantum simulations. It discusses the number of qubits, operations, and steps required for different types of simulations, and highlights the importance of fault tolerance and decoherence in practical quantum simulations. Additionally, it explores the use of quantum information-inspired algorithms for classical simulation of quantum systems, which can provide more efficient methods for certain problems. Overall, the review emphasizes the potential of quantum simulation to advance research in various scientific disciplines and the ongoing efforts to develop practical quantum simulation techniques.The article provides a comprehensive overview of quantum simulation, a method to study quantum systems by using other controllable quantum systems. Quantum simulation is particularly useful for systems with large numbers of particles, where classical computers struggle due to the exponential growth in computational complexity. The authors discuss the challenges and potential applications of quantum simulation in various fields such as condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation can be implemented in two main ways: digital quantum simulation (DQS) and analog quantum simulation (AQS). DQS involves encoding the wavefunction of the system into a quantum register and performing unitary transformations to simulate the system's evolution. AQS, on the other hand, uses a controllable quantum system that mimics the dynamics of another quantum system. Both methods have their advantages and limitations, and the choice between them depends on the specific problem and the capabilities of the simulator. The article also covers resource estimation, which is crucial for determining the feasibility of quantum simulations. It discusses the number of qubits, operations, and steps required for different types of simulations, and highlights the importance of fault tolerance and decoherence in practical quantum simulations. Additionally, it explores the use of quantum information-inspired algorithms for classical simulation of quantum systems, which can provide more efficient methods for certain problems. Overall, the review emphasizes the potential of quantum simulation to advance research in various scientific disciplines and the ongoing efforts to develop practical quantum simulation techniques.