Copyright © 2017 John Wiley & Sons, Ltd. The intensity in the requirements of Internet of Things and mobile internet makes the efficiency of fifth-generation (5G) wireless communications very challenging to achieve. Accomplishing the drastically increasing demand of massive connectivity and high spectral efficiency is a strenuous task. Because of the very large number of devices, 5G wireless communication systems are inevitable to satisfy the traffic requirements. Recently, nonorthogonal multiple-access (NOMA) schemes are immensely being explored to address the challenges in 5G, which include effective bandwidth utilization, support for a massive number of devices, and low latency. This paper provides the reader with a holistic view of multiple-access schemes, methods, and strategies for optimization in NOMA. First, we discuss the taxonomy of multiple-access schemes in the literature; then, we provide a detailed discussion of objectives, constraints, problem types, and solution approaches for NOMA. This paper also discusses the decoding methods and key performance indicators used in NOMA. Finally, we outline future research directions.