The continuous deployment of network services over the wide range of public and private networks has led to transactions and services that include personal, and sometimes quite sensitive, data. Examples of services include: pay-per-view, cable telephony, bill payments by phone, credit card charging, and Internet banking. Such services require significant effort not only to protect the sensitive data involved in the transactions and services but to ensure integrity and availability of network services as well. The requirement for employing heterogeneous networks and systems becomes increasingly important, and as the view of traditional distributed systems has changed to a network centric view in all types of application networks, therefore, the complexity of these systems has led to significant security flaws and problems. Existing conventional approaches for security service development over such complex and most often heterogeneous networks and systems are not satisfying and cannot meet users and applications needs; therefore, several approaches have been developed to provide security at various levels and degrees, such as: secure protocols, secure protocol mechanisms, secure services, firewalls, Intrusion Detection Systems (IDS), and later Intrusion Prevention System (IPS), etc. This chapter considers and addresses several aspects of network security in an effort to provide a publication that summarizes the current status and the promising and interesting future directions and challenges. The authors try to present the state-of-the-art in this chapter for the following topics: Internet security, secure services, security in mobile systems and trust, anonymity, and privacy.