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By combining the concepts of superposition coding at the transmitter(s) and successive interference cancellation (SIC) at the receiver(s), non-orthogonal multiple access (NOMA) has recently emerged as a promising multiple access technique for 5G wireless technology. In this article, we first discuss the fundamentals of uplink and downlink NOMA transmissions and outline their key distinctions (in terms of implementation complexity, detection and decoding at the SIC receiver(s), incurred intra-cell and inter-cell interferences). Later, for both downlink and uplink NOMA, we theoretically derive the NOMA dominant condition for each individual user in a two-user NOMA cluster. NOMA dominant condition refers to the condition under which the spectral efficiency gains of NOMA are guaranteed compared to conventional orthogonal multiple access (OMA). The derived conditions provide direct insights on selecting appropriate users in two-user NOMA clusters. The conditions are distinct for uplink and downlink as well as for each individual user. Numerical results show the significance of the derived conditions for the user selection in uplink/downlink NOMA clusters and provide a comparison to the random user selection. A brief overview of the recent research investigations is then provided to highlight the existing research gaps. Finally, we discuss the potential applications and key challenges of NOMA transmissions.