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A wide range of social, technological and communication systems can be described as complex networks. Scale-free networks are one of the well known classes of complex networks in which nodes' degrees follow a power-law distribution. The design of scalable, adaptive and resilient routing schemes in such networks is very challenging. In this article we present an overview of required routing functionality, categorize the potential design dimensions of routing protocols among existing routing schemes, and analyze experimental results and analytical studies performed so far to identify the main trends/trade-offs and draw main conclusions. Besides traditional schemes such as hierarchical/shortest-path path-vector routing, the article pays attention to advances in compact routing and geometric routing since they are known to significantly improve scalability in terms of memory space. The identified trade-offs and the …