Variational Quantum Algorithms (VQAs) are a promising strategy for leveraging current quantum devices to achieve quantum advantage. VQAs use classical optimizers to train parametrized quantum circuits, addressing the limitations of qubit numbers and circuit depth in NISQ devices. This review covers the fundamental concepts and tools of VQAs, including cost functions, ansatzes, gradients, and optimizers. It highlights the versatility of VQAs in solving a wide range of problems, such as finding ground and excited states, simulating quantum systems, and solving linear systems of equations. The article also discusses specific VQA implementations like the Variational Quantum Eigensolver (VQE) and its variants, as well as applications in dynamical quantum simulation and variational fast forwarding. Despite challenges in trainability, accuracy, and efficiency, VQAs remain a key area of research for achieving practical quantum advantage.Variational Quantum Algorithms (VQAs) are a promising strategy for leveraging current quantum devices to achieve quantum advantage. VQAs use classical optimizers to train parametrized quantum circuits, addressing the limitations of qubit numbers and circuit depth in NISQ devices. This review covers the fundamental concepts and tools of VQAs, including cost functions, ansatzes, gradients, and optimizers. It highlights the versatility of VQAs in solving a wide range of problems, such as finding ground and excited states, simulating quantum systems, and solving linear systems of equations. The article also discusses specific VQA implementations like the Variational Quantum Eigensolver (VQE) and its variants, as well as applications in dynamical quantum simulation and variational fast forwarding. Despite challenges in trainability, accuracy, and efficiency, VQAs remain a key area of research for achieving practical quantum advantage.