<p>Simulating quantum systems with high accuracy remains one of the fundamental challenges in science, with applications ranging from drug discovery to materials design. In particular, quantum chemical simulations play a pivotal role in advancing fields such as chemistry, materials science, and biology. While classical computational methods have achieved considerable success, their ability to simulate complex quantum systems often requires several approximations, making the results inaccurate. Quantum computers are anticipated to overcome these challenges by providing more accurate simulations of complex quantum systems. However, the current generation of quantum devices is limited by noise and decoherence, restricting their practical applications. To overcome these limitations, hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) have been developed. In this review, we discuss several notable examples where VQE and its variants have been successfully applied to quantum chemistry problems, highlighting both the current capabilities and the future potential of quantum computing for quantum chemical applications.</p>