Efficient light energy transfer between optical wave guides has been a critical issue in various areas of photonics and optoelectronics. Especially, the light coupling between optical fibers and integrated wave-guide structures provides essential input-output interfaces for photonic integrated circuits (PICs) and plays a crucial role in reliable optical signal transport for a number of applications, such as optical interconnects, optical switching, and integrated quantum optics. Significant efforts have been made to improve light coupling properties, including coupling efficiency, bandwidth, polarization dependence, alignment tolerance, as well as packing density. In this review article, we survey three major light coupling methods between optical fibers and integrated wave-guides: end-fire coupling, diffraction grating-based coupling, and adiabatic coupling. Although these waveguide coupling methods are different in terms of their operating principles and physical implementations, they have gradually adopted various nanophotonic structures and techniques to improve the light coupling properties as our understanding to the behavior of light and nano-fabrication technology advances. We compare the pros and cons of each light coupling method and provide an overview of the recent developments in waveguide coupling between optical fibers and integrated photonic circuits.