Since the well-established navigation systems such as GPS are ineffective in indoor environments, research into developing novel indoor positioning technologies has emerged in recent years. While several technologies are being investigated, a practical and reliable indoor positioning system is yet to emerge. Indoor positioning using light signals holds a great potential to provide a reliable solution to the indoor positioning problem. This paper presents a comprehensive review of the available literature on light-based indoor positioning systems. The paper establishes a classification based on the design of various light-based indoor positioning (LIP) systems, and discusses their key components including hardware, software and algorithms. The limitations and challenges of the LIP systems are discussed in details, and current published solutions are presented. The review also provides a comparison between LIP systems and other optical positioning systems, and identifies the associated research gaps. Finally, based on the identified gaps, the future research directions in both LIP systems and other optical positioning systems are presented.