Fifth generation (5G) wireless networks face various challenges in order to support largescale heterogeneous traffic and users, therefore new modulation and multiple access (MA) schemes are being developed to meet the changing demands. As this research space is ever increasing, it becomes more important to analyze the various approaches, therefore, in this article we present a comprehensive overview of the most promising Multiple Access schemes for 5G networks. Our article focuses on various types of non-orthogonal multiple access (NOMA) techniques. Specifically, we first introduce different types of modulation schemes, potential for OMA. We then pay close attention to various types of NOMA candidates, including power-domain NOMA, code-domain NOMA, and NOMA multiplexing in multiple domains. From this exploration, we can identify the opportunities and challenges that will have the most significant impacts on modulation and MA designs for 5G networks.