The proliferation of connected devices and emergence of internet-of-everything represent a major challenge for broadband wireless networks. This requires a paradigm shift towards the development of innovative technologies for next generation wireless systems. One of the key challenges is the scarcity of spectrum, owing to the unprecedented broadband penetration rate in recent years. A promising solution is the proposal of visible light communications (VLC), which explores the unregulated visible light spectrum to enable high-speed communications, in addition to efficient lighting. This solution offers a wider bandwidth that can accommodate ubiquitous broadband connectivity to indoor users and offload data traffic from cellular networks. Although VLC is secure and able to overcome the shortcomings of RF systems, it suffers from several limitations, e.g., limited modulation bandwidth. In this respect, solutions have been proposed recently to overcome this limitation. In particular, most common orthogonal and non-orthogonal multiple access techniques initially proposed for RF systems, e.g., space-division multiple access (SDMA) and NOMA, have been considered in the context of VLC. In spite of their promising gains, the performance of these techniques is somewhat limited. Consequently, in this article a new and generalized multiple access technique, called rate-splitting multiple access (RSMA), is introduced and investigated for the first time in VLC networks. We first provide an overview of the key multiple access technologies used in VLC systems. Then, we propose the first comprehensive approach to the integration of RSMA with VLC systems. In our proposed framework, SINR expressions are derived and used to evaluate the weighted sum rate (WSR) of a two-user scenario. Our results illustrate the flexibility of RSMA in generalizing NOMA and SDMA, and its WSR superiority in the VLC context.