Visible light communication (VLC) has become a promising technology for high data rate communications and an attractive complementary to conventional radio frequency (RF) communication. VLC is a secure, energy efficient and cost-effective technology that exploits the existing infrastructure, particularly in indoor environments, for wireless data transmission. Nevertheless, the main limitation of developing high data rate VLC links is the narrow modulation bandwidth of light-emitting diodes (LEDs), which is in the megahertz range. The power domain nonorthogonal multiple access (PD-NOMA) scheme is envisioned to address several challenges in VLC systems. In this paper, we present a detailed overview of PD-NOMA based VLC systems. Moreover, we introduce insights on some PD-NOMA VLC system constraints and challenges such as power allocation, clipping effect, MIMO and security. Finally, we provide open research problems as well as possible directions for future research to pave the way for the implementation of PD-NOMA VLC systems.