The proliferation of mobile Internet and connected devices, offering a variety of services at different levels of performance, represents a major challenge for the fifth generation wireless networks and beyond. This requires a paradigm shift towards the development of key enabling techniques for the next generation wireless networks. In this respect, visible light communication (VLC) has recently emerged as a new communication paradigm that is capable of providing ubiquitous connectivity by complementing radio frequency communications. One of the main challenges of VLC systems, however, is the low modulation bandwidth of the light-emitting-diodes, which is in the megahertz range. This article presents a promising technology, referred to as optical- non-orthogonal multiple access (O-NOMA), which is envisioned to address the key challenges in the next generation of wireless networks. We provide a detailed overview and analysis of the state-of-the-art integration of O-NOMA in VLC networks. Furthermore, we provide insights on the potential opportunities and challenges as well as some open research problems that are envisioned to pave the way for the future design and implementation of O-NOMA in VLC systems.