Digital quantum simulation (DQS) is a promising approach for simulating quantum many-body systems on near-term quantum computers. While analog quantum simulation has demonstrated quantum advantage, DQS has gained attention due to the availability of general-purpose quantum computers. This perspective reviews current approaches in DQS, comparing non-variational and variational methods, and identifies hardware and algorithmic challenges. It argues that qualitative problems are more suitable for near-term devices than those aiming for quantitative accuracy. DQS uses gate-based quantum computers to simulate quantum systems by discretizing time evolution and implementing it with quantum gates. It offers universal simulation of many-body dynamics, especially for systems not suitable for analog simulators. Recent advances include simulations of quantum many-body systems, topological systems, many-body localization, and time crystals. These simulations have been performed on various platforms, including superconducting qubits, trapped ions, and photonic circuits. Variational quantum algorithms, which combine quantum and classical computation, have shown promise in DQS. These algorithms use parameterized quantum circuits to approximate eigenstates and simulate quantum many-body dynamics. However, they face challenges such as barren plateaus and the need for high-fidelity quantum operations. Error mitigation techniques, including readout error mitigation, zero noise extrapolation, and optimized circuit compilation, are crucial for improving the accuracy of DQS on noisy quantum computers. Despite progress, DQS faces significant challenges, including noise, decoherence, and limited qubit numbers. Current hardware limitations restrict the size of systems that can be simulated, and achieving fault-tolerant quantum computation remains a distant goal. Nevertheless, DQS has the potential to provide insights into complex quantum systems, such as topological phases, many-body localization, and quantum many-body dynamics. Future research should focus on developing more efficient algorithms, improving hardware performance, and exploring new quantum platforms to advance DQS.Digital quantum simulation (DQS) is a promising approach for simulating quantum many-body systems on near-term quantum computers. While analog quantum simulation has demonstrated quantum advantage, DQS has gained attention due to the availability of general-purpose quantum computers. This perspective reviews current approaches in DQS, comparing non-variational and variational methods, and identifies hardware and algorithmic challenges. It argues that qualitative problems are more suitable for near-term devices than those aiming for quantitative accuracy. DQS uses gate-based quantum computers to simulate quantum systems by discretizing time evolution and implementing it with quantum gates. It offers universal simulation of many-body dynamics, especially for systems not suitable for analog simulators. Recent advances include simulations of quantum many-body systems, topological systems, many-body localization, and time crystals. These simulations have been performed on various platforms, including superconducting qubits, trapped ions, and photonic circuits. Variational quantum algorithms, which combine quantum and classical computation, have shown promise in DQS. These algorithms use parameterized quantum circuits to approximate eigenstates and simulate quantum many-body dynamics. However, they face challenges such as barren plateaus and the need for high-fidelity quantum operations. Error mitigation techniques, including readout error mitigation, zero noise extrapolation, and optimized circuit compilation, are crucial for improving the accuracy of DQS on noisy quantum computers. Despite progress, DQS faces significant challenges, including noise, decoherence, and limited qubit numbers. Current hardware limitations restrict the size of systems that can be simulated, and achieving fault-tolerant quantum computation remains a distant goal. Nevertheless, DQS has the potential to provide insights into complex quantum systems, such as topological phases, many-body localization, and quantum many-body dynamics. Future research should focus on developing more efficient algorithms, improving hardware performance, and exploring new quantum platforms to advance DQS.