Cognitive radio has been considered as a promising technology for improving spectrum utilization. To further enhance the efficiency of packets/messages transportation (i.e. network utilization), cognitive radio networks (CRN) has been proposed to integrate existing communication system/networks with cognitive radios systems/networks. Due to the temporarily availability and unidirectional properties of links in CRN, new routing problems that degrade network efficiency need to be considered. In this thesis, we define these problems from three perspectives: route discovery, packet forwarding and route maintenance. When discovering routes in CRN, the routing messages can be delayed and/or dropped by the temporarily unidirectional links, which can delay or even fail the route discovery procedure. Similar situations occur in packet forwarding when route diversity is low. When maintaining a route, the unidirectional property of CRN links makes the reverse route(s) from the downstream node to the upstream node for each link on the route necessary. Due to the delay and/or loss of feedback information on the reverse routes, the confirmation of link status can often be delayed and misled, which can degrade the routing performance. All problems are defined and verified in this thesis. Then we propose two solutions to alleviate these problems – non-disjoint multipath discovery algorithm and local proactive reverse route maintenance algorithm.