Applying the learning mechanism of natural living beings to endow intelligent robots with humanoid perception and decision-making wisdom becomes an important force to promote the revolution of science and technology in robot domains. Advances in reinforcement learning (RL) over the past decades have led robotics to be highly automated and intelligent, which ensures safety operation instead of manual work and implementation of more intelligence for many challenging tasks. As an important branch of machine learning, RL can realize sequential decision-making under uncertainties through end-to-end learning and has made a series of significant breakthroughs in robot applications. In this review article, we cover RL algorithms from theoretical background to advanced learning policies in different domains, which accelerate to solving practical problems in robotics. The challenges, open issues, and our thoughts on future research directions of RL are also presented to discover new research areas with the objective to motivate new interest.