Combinatorial optimization problems are difficult to solve due to the space explosion in an exhaustive search. Using Ising model-based solvers can efficiently find near-optimal solutions by minimizing the energy of a nonlinear Hamiltonian system. In contrast to Ising machines based on quantum mechanics, classical Ising machines using conventional technologies, such as the complementary metal–oxide–semiconductor, offer efficient implementations with a competitive performance. In this paper, we briefly review recently developed simulation algorithms of classical Ising machines. These algorithms are classified by considering various inherent mechanisms in the simulation of physical properties of spins. Then, strategies to improve the simulation efficiency are discussed by generalizing the characteristics and behaviours of the Ising model. These simulation algorithms are key to improving the efficiency of Ising machines in solving combinatorial optimization problems.