Robotic equipment has been playing a central role since the proposal of smart manufacturing. Since the beginning of the first integration of industrial robots into production lines, industrial robots have enhanced productivity and relieved humans from heavy workloads significantly. Towards the next generation of manufacturing, this review first introduces the comprehensive background of smart robotic manufacturing within robotics, machine learning, and robot learning. Definitions and categories of robot learning are summarised. Concretely, imitation learning, policy gradient learning, value function learning, actor-critic learning, and model-based learning as the leading technologies in robot learning are reviewed. Training tools, benchmarks, and comparisons amongst different robot learning methods are delivered. Typical industrial applications in robotic grasping, assembly, process control, and industrial human-robot collaboration are listed and discussed. Finally, open problems and future research directions are summarised.