1 Introduction  
2 Quantum Simulation  
2.1 Digital Quantum Simulation  
2.2 Analog Quantum Simulation  
2.3 Digital-Analog Quantum Simulation  
3 Transformation and Mapping Schemes  
3.1 Jordan-Wigner Transformation  
3.2 Holstein-Primakoff Transformation  
3.3 Bravyi-Kitaev Transformation  
4 State Preparation  
Ground State Preparation  
Excited State Preparation  
Thermal State Preparation  
Configuration Method for State Preparation  
5 Hamiltonian Simulation  
5.1 Product Formula Algorithm  
5.2 Taylor Series Algorithm  
5.3 Quantum Signal Processing Algorithm  
6 Emerging Potential Domains for Quantum Simulations  
6.1 Condensed Matter  
6.2 Light-Matter Interaction  
6.3 Open Quantum Systems  
6.4 Quantum Chemistry  
6.5 Bioinformatics  
7 Error Mitigation  
8 Software Tool Sets  
9 Concluding Remarks