Variational quantum algorithms (VQAs) are a promising approach for achieving quantum advantage on near-term quantum computers, which are limited by noise and qubit count. VQAs use a classical optimizer to train a parametrized quantum circuit, allowing them to address the constraints of current quantum devices. They have been proposed for a wide range of applications, including simulating quantum systems and solving large-scale linear algebra problems. Despite their potential, challenges remain in terms of trainability, accuracy, and efficiency. This review discusses the key concepts, tools, and applications of VQAs, highlighting their role in achieving quantum advantage. VQAs include various ansatzes, such as hardware-efficient, UCC, QAOA, and variational Hamiltonian ansatzes, each tailored for specific tasks. The cost function and gradients are crucial for optimization, with methods like the parameter-shift rule enabling efficient gradient computation. Optimizers such as gradient descent and meta-learning are used to improve performance. Applications of VQAs include finding ground and excited states, dynamical quantum simulation, and other quantum computing tasks. The review also addresses challenges such as barren plateaus and hardware noise, and discusses strategies to overcome them. Overall, VQAs represent a key strategy for leveraging current quantum hardware to achieve quantum advantage.Variational quantum algorithms (VQAs) are a promising approach for achieving quantum advantage on near-term quantum computers, which are limited by noise and qubit count. VQAs use a classical optimizer to train a parametrized quantum circuit, allowing them to address the constraints of current quantum devices. They have been proposed for a wide range of applications, including simulating quantum systems and solving large-scale linear algebra problems. Despite their potential, challenges remain in terms of trainability, accuracy, and efficiency. This review discusses the key concepts, tools, and applications of VQAs, highlighting their role in achieving quantum advantage. VQAs include various ansatzes, such as hardware-efficient, UCC, QAOA, and variational Hamiltonian ansatzes, each tailored for specific tasks. The cost function and gradients are crucial for optimization, with methods like the parameter-shift rule enabling efficient gradient computation. Optimizers such as gradient descent and meta-learning are used to improve performance. Applications of VQAs include finding ground and excited states, dynamical quantum simulation, and other quantum computing tasks. The review also addresses challenges such as barren plateaus and hardware noise, and discusses strategies to overcome them. Overall, VQAs represent a key strategy for leveraging current quantum hardware to achieve quantum advantage.