Non-orthogonal multiple access (NOMA) is promoted as a key component of 5G cellular networks. As the name implies, NOMA operation introduces intracell interference (i.e., interference arising within the cell) to the cellular operation. The intracell interference is managed by careful NOMA design (e.g., user clustering and resource allocation) along with successive interference cancellation. However, most of the proposed NOMA designs are agnostic to intercell interference (i.e., interference from outside the cell), which is a major performance limiting parameter in 5G networks. This article sheds light on the drastic negative-impact of intercell interference on the NOMA performance and advocates interference-aware NOMA design that jointly accounts for both intracell and intercell interference. To this end, a case study for fair NOMA operation is presented and intercell interference mitigation techniques for NOMA networks are discussed. This article also investigates the potential of integrating NOMA with two important 5G transmission schemes, namely, full duplex and device-to-device communication. This is important since the ambitious performance defined by the 3rd Generation Partnership Project (3GPP) for 5G is foreseen to be realized via seamless integration of several new technologies and transmission techniques.