Background: The proliferation of cloud providers and provisioning levels has opened a space for cloud brokerage services. Brokers intermediate between cloud customers and providers to assist the customer in selecting the most suitable cloud service, helping to manage the dimensionality, heterogeneity, and uncertainty associated with cloud services. Objective: This paper identifies and classifies approaches to realise cloud brokerage. By doing so, this paper presents an understanding of the state of the art and a novel taxonomy to characterise cloud brokers. Method: We conducted a systematic literature survey to compile studies related to cloud brokerage and explore how cloud brokers are engineered. We analysed the studies from multiple perspectives, such as motivation, functionality, engineering approach, and evaluation methodology. Results: The survey resulted in a knowledge base of current proposals for realising cloud brokers. The survey identified surprising differences between the studies' implementations, with engineering efforts directed at combinations of market-based solutions, middlewares, toolkits, algorithms, semantic frameworks, and conceptual frameworks. Conclusion: Our comprehensive meta-analysis shows that cloud brokerage is still a formative field. There is no doubt that progress has been achieved in the field but considerable challenges remain to be addressed. This survey identifies such challenges and directions for future research.