The evolving explosion in high data rate services and applications will soon require the use of untapped, abundant unregulated spectrum of the visible light for communications to adequately meet the demands of the fifth-generation (5G) mobile technologies. Radio-frequency (RF) networks are proving to be scarce to cover the escalation in data rate services. Visible light communication (VLC) has emerged as a great potential solution, either in replacement of, or complement to, existing RF networks, to support the projected traffic demands. Despite the prolific advantages of VLC networks, VLC faces many challenges that must be resolved in the near future to achieve a full standardization and to be integrated to future wireless systems. Here, we review the new, emerging research in the field of VLC networks and lay out the challenges, technological solutions, and future work predictions. Specifically, we first review the VLC channel capacity derivation, discuss the performance metrics and the associated variables; the optimization of VLC networks are also discussed, including resources and power allocation techniques, user-to-access point (AP) association and APs-to-clustered-users-association, APs coordination techniques, non-orthogonal multiple access (NOMA) VLC networks, simultaneous energy harvesting and information transmission using the visible light, and the security issue in VLC networks. Finally, we propose several open research problems to optimize the various VLC networks by maximizing either the sum rate, fairness, energy efficiency, secrecy rate, or harvested energy.