The article provides a comprehensive overview of digital quantum simulation (DQS) on emerging quantum processors, highlighting its potential and challenges. DQS, which uses gate-based quantum computers to simulate quantum systems, has gained significant attention due to the availability of general-purpose quantum computers. The review covers various approaches, including non-variational and variational methods, and discusses the advances in DQS, such as the Trotterized time evolution and variational quantum eigensolver (VQE). It emphasizes the importance of addressing hardware and algorithmic challenges, such as noise and decoherence, and explores the potential applications of DQS in understanding complex quantum systems, topological phases, many-body localization, and time crystals. The article concludes by discussing the broader implications of DQS and the need to focus on problems that involve fundamental principles and qualitative understanding, rather than purely quantitative accuracy improvements.The article provides a comprehensive overview of digital quantum simulation (DQS) on emerging quantum processors, highlighting its potential and challenges. DQS, which uses gate-based quantum computers to simulate quantum systems, has gained significant attention due to the availability of general-purpose quantum computers. The review covers various approaches, including non-variational and variational methods, and discusses the advances in DQS, such as the Trotterized time evolution and variational quantum eigensolver (VQE). It emphasizes the importance of addressing hardware and algorithmic challenges, such as noise and decoherence, and explores the potential applications of DQS in understanding complex quantum systems, topological phases, many-body localization, and time crystals. The article concludes by discussing the broader implications of DQS and the need to focus on problems that involve fundamental principles and qualitative understanding, rather than purely quantitative accuracy improvements.