The ongoing development of mobile communication networks to support a wide range of superfast broadband services has led to massive capacity demand. This problem is expected to be a significant concern during the deployment of the 5G wireless networks. The demand for additional spectrum to accommodate mobile services supporting higher data rates and having lower latency requirements, as well as the need to provide ubiquitous connectivity with the advent of the Internet of Things (IoT) sector, is likely to considerably exceed the supply, based on the current policy of exclusive spectrum allocation to mobile cellular systems. Hence, the imminent spectrum shortage has introduced a new impetus to identify practical solutions to make the most efficient use of the scarce licensed bands in a shared manner. Recently, the concept of dynamic spectrum sharing has received considerable attention from regulatory bodies and governments globally, as it could potentially open new opportunities for mobile operators to exploit spectrum bands whenever they are underutilised by their owners, subject to service level agreements. Although various sharing paradigms have been proposed and discussed, the impact and performance gains of different schemes can be scenario-specific and vary depending on the nature of the sharing parties, the level of sharing and spectrum access scheme. In this survey, we describe the main concepts of dynamic spectrum sharing, different sharing scenarios, as well as the major challenges associated with sharing licensed bands. Finally, we conclude this survey paper with open research challenges and suggest some future research directions