Fifth-generation wireless communications provide several benefits, including high throughput, lower latency, massive connectivity, considerable improvement in the number of users, higher base station capacity, and achieved quality of service. Non-orthogonal multiple access, an effective approach for sharing the same radio resources, has been highlighted as a viable technology in the fifth-generation wireless networks to achieve the demands of available bandwidth, user connectivity, and application latency. Non-orthogonal multiple access and heterogeneous networks have recently emerged as promising network infrastructures for enhancing the spectrum capacity and accommodating more users by sharing the same resources with high throughput. This potential capability has made the non-orthogonal multiple access–enabled heterogeneous networks a new research topic in the modern era. In this survey, the concept of non-orthogonal multiple access and its significance in different emerging technologies has been well explored. Furthermore, this survey covers a systematic overview of the state-of the-art techniques based on non-orthogonal multiple access–enabled heterogeneous networks and devising taxonomy for uplink non-orthogonal multiple access–enabled heterogeneous networks. In addition, this survey provides critical insights and identifies several open research challenges considering the uplink non-orthogonal multiple access–enabled heterogeneous networks.