The ever-increasing demand of mobile Internet and multimedia services poses unique and significant challenges for current and future generation wireless networks. These challenges are mainly relating to the support of massive ubiquitous connectivity, low latency and highly efficient utilization of spectrum resources. Therefore, it is vital to consider them extensively prior to design and deployment of future wireless networks. To this end, the present article provides a comprehensive overview of a particularly promising and effective wireless technology, namely, visible light communication (VLC). In this context, we initially provide a thorough overview of frequency domain multiple access techniques for single and multi-carrier systems, which is then followed by an in depth discussion on the technical considerations of optical code division multiple access techniques and their adoption in indoor VLC applications. Furthermore, we address space division multiple access and, finally, we revisit and analyze the distinct characteristics of a new technology, namely, non-orthogonal multiple access, which has been proposed recently as a particularly effective solution.