Routing for shared protection has received a lot of interest in the last few years. A large number of the studies focus on minimizing the network transport capacity in a static routing framework. A smaller number of studies have been conducted on dynamic routing. Most of them are limited to single-domain networks and do not meet the scalability requirements of multi-domain networks. This paper reviews the recent works in dynamic routing for shared protection in multi-domain networks, and proposes a quantitative comparison amongst the most efficient approaches. Some of the remaining challenges are discussed at the end of the paper.