This paper studies the transmission rates and physical layer security of cooperative relay networks. For any relay network, there are natural information theoretic cut-set bounds, which upper bound the transmission rates. We further tighten the outer bounds on rate regions. We also study the achievable rate regions in consideration of physical layer security. We analyze two cross-group cooperative strategies with decodeand- forward relaying and compress-and-forward relaying respectively. We can use the decode-and-forward scheme only if the users which have both good communication channels from the source and high levels of security clearance are selected to serve as relays; otherwise, we cannot achieve physical layer security. While the compress-and-forward scheme is used, physical layer security can be achieved even though the relays have lower security clearance than the destinations.