As the prospect of commercial quantum computers turns ever more real in recent times, research in quantum algorithms becomes the center of attention. Due to the strong parallelism of quantum computing in Hilbert space, ordinarily intractable calculation problems could now be solved very efficiently with non-classical means. To exploit parallelism, creative quantum algorithms are required so that efficient quantum oracles can be tailor-designed to specific computation needs. Therefore, in the quest for quantum supremacy, quantum algorithms and their related applications are as important as the quantum computer hardware. This article covers the basic concepts of quantum computation and reviews some important quantum algorithms and their applications.