As the current quantum computers are still noisy and do not accommodate sufficiently many qubits for practical programs or quantum circuit developments, in order to make sure the correctness and properties of quantum circuits, it makes sense to simulate them on top of classical computers, where no error is expected. There have been proposed varieties of algorithms/methods by which behaviors of given quantum circuits can be generated, i.e., quantum circuit simulation. We review those techniques with discussions of their advantages/disadvantages, and give their evaluations and comparisons by actually running them on benchmark circuits. Finally, we discuss extensions of quantum circuit simulations including symbolic simulationsSymbolic simulation for more robust verificationVerification.