With the fast development of wireless networks and devices, MobileIP is expected to be used widely so that mobile users can accessthe Internet anywhere, anytime without interruption. However, someproblems, such as firewall traversal and use of private IPaddresses, restrict use of Mobile IP. The objective of this thesisis to design original schemes that can enable a mobile node atabroad to access its home network as well as the Internet securelyand that can help Mobile IP to be used widely and commercially.Our solutions are secure, efficient, and scalable. They can beimplemented and maintained easily. In this thesis, we mainlyconsider Mobile IPv4, instead of Mobile IPv6. Three researchtopics are discussed. In each topic, the challenges areinvestigated and the new solutions are presented.The first research topic solves the firewall traversal problems inMobile IP. A mobile node cannot access its firewall-protected homenetwork if it fails the authentication by the firewall. We proposethat an IPsec tunnel be established between the firewall and theforeign agent for firewall traversal and that an IPsec transportsecurity association be shared by the mobile node and acorrespondent node for end-to-end security.The second topic researches further on firewall traversal problemsand investigates the way of establishing security associationsamong network entities. A new security model and a new keydistribution method are developed. With the help of the securitymodel and keys, the firewall and the relevant network entities setup IPsec security associations to achieve firewall traversal.A mobile node from a private home network cannot communicate withother hosts with its private home address when it is visiting apublic foreign network. A novel and useful solution is presentedin the third research topic. We suggest that the mobile node useits Network Access Identifier (NAI) as its identification andobtain a public home address from its home agent. In addition, anew tunnel between the mobile node and its home agent is proposed.