Developing wireless communication technologies is an ongoing process to satisfy the requirements of new applications and the increasing proliferation of interconnected devices. Using non-orthogonal multiple access (NOMA) and backscatter communication (BC) has surfaced as an advantageous approach for enhancing energy efficiency (EE), maximizing sum rates, ensuring security, and optimizing resource allocation. NOMA permits multiple users to share time and frequency resources even without the requirement of antenna arrays, whereas BC employs ambient RF signals for low-power communication. By integrating the advantages of NOMA and BC, NOMA-based BC provides a solution for future energyefficient and low-power networks. Despite its potential, there is a lack of a comprehensive overview of NOMA-BC, necessitating a systematic survey that covers its principles, applications, challenges, and future directions. This survey aims to bridge the gap by exploring NOMA-BC within B5G and 6G networks. We delve into its technical aspects, performance optimization techniques, and real-world applications to enhance understanding and knowledge. First, we cover topics such as enhancing EE, maximizing the sum rates, ensuring security, and optimizing resource allocation. Our primary goal is to provide researchers and practitioners with valuable insights that enable them to grasp the capabilities and benefits of NOMA-BC. To achieve this, we comprehensively analyze various schemes' performance by presenting detailed summary tables. These analyses cover a range of scenarios, methods, and objectives, focusing on emerging B5G technologies such as reconfigurable intelligent surfaces (RIS), visible light communication (VLC), and unmanned aerial vehicle (UAV) communication. By examining NOMA-BC's effectiveness within these contexts, we aim to provide a holistic view of its potential and applicability in diverse technological domains. Moreover, our survey identifies and discusses open research challenges and proposes future directions to guide researchers toward unexplored areas and facilitate advancements in NOMA-BC.