This article presents a detailed survey on both asynchronous and synchronous Optical Code-Division Multiple-Access (OCDMA) systems based on 1-D, 2-D, and 3-D codes, distinctively. Accordingly, different coding schemes along with their multiplexing capacity, correlation features, advantages and drawbacks are addressed and benchmarked. Additionally, different detection techniques such as direct and coherent detection and their capability to handle Multiple Access-Interference are also discussed. Furthermore, the main OCDMA systems from the last two decades are summarized considering their coding schemes, performance, device components, and applications. Therefore, a new comparative study in terms of spectral efficiency and bit error rate for 1-D, 2-D, and 3-D asynchronous and synchronous OCDMA systems is carried out. Numerical results shown that the 3-D MD code stands out among the codes with superior performance as well as support to higher data rates and number of users.