In recent times, there have been many advances in the field of information theory and wireless ad hoc network technologies. Regarding information theory progression and its connection with wireless ad hoc networks, this study presents fundamental concepts related to the application of the state-of-the-art Network Coding (NC) within wireless ad hoc networks in the context of routing. To begin with, this paper briefly describes opportunistic routing and identifies differentiation between NC-aware and NC-based routing mechanisms in wireless ad hoc networks. However, our main focus is to provide a survey of available NC-aware routing protocols that make forwarding decisions based on the information of available coding opportunities across several routes within wireless ad hoc networks. The taxonomy and characteristics of various representative NC-aware routing protocols will also be discussed. In summary, we provide a comparison of available NC-aware routing schemes and conclude that NC-aware routing techniques have several advantages over traditional routing in terms of high throughput, high reliability, and lower delay in a wireless scenario. To the best of our knowledge, this work is the first that provides comprehensive discussion about NC-aware routing protocols.