The unprecedented growth of the Internet over the last years, and the expectation of an even faster increase in the numbers of users and networked systems, resulted in the Internet assuming its position as a mass communication medium. At the same time, the emergence of an increasingly large number of application areas and the evolution of the networking technology suggest that in the near future the Internet may become the single integrated communication infrastructure. However, as the dependence on the networking infrastructure grows, its security becomes a major concern, in light of the increased attempt to compromise the infrastructure. In particular, the routing operation is a highly visible target that must be shielded against a wide range of attacks. The injection of false routing information can easily degrade network performance, or even cause denial of service for a large number of hosts and networks over a long period of time. Different approaches have been proposed to secure the routing protocols, with a variety of countermeasures, which, nonetheless, have not eradicated the vulnerability of the routing infrastructure. In this article, we survey the up-to-date secure routing schemes that appeared over the last few years. Our critical point of view and thorough review of the literature are an attempt to identify directions for future research on an indeed difficult and still largely open problem.