Non-orthogonal multiple access (NOMA) is a potential enabler for the development of 5G and beyond wireless networks. By allowing multiple users to share the same time and frequency, NOMA can scale up the number of served users, increase the spectral efficiency, and improve user-fairness compared to existing orthogonal multiple access (OMA) techniques. While single-cell NOMA has drawn significant attention recently, much less attention has been given to multi-cell NOMA. This article discusses the opportunities and challenges of NOMA in a multi-cell environment. As the density of base stations and devices increases, inter-cell interference becomes a major obstacle in multi-cell networks. As such, identifying techniques that combine interference management approaches with NOMA is of great significance. After discussing the theory behind NOMA, this paper provides an overview of the current literature and discusses key implementation and research challenges, with an emphasis on multi-cell NOMA.