We can observe the exploding use of the Internet for various applications, ranging from ordinary E-mail exchange and all kinds of net-oriented databases, to large distributed cooperative projects. All these emerging activities heavily rely on the continuous availability of the Internet services, with regard to their proper function as well as to their timely execution. Therefore, it is felt to be extremely necessary to make especially the entire communication within the system as robust as possible. We discuss these dependability problems in detail and present a survey of research approaches to deal with them. Thereby, the focus of attention is the discussion of routing, ie, the propagation of information between non-adjacent nodes, at three levels of the Web communication: in local networks connected to server nodes, in the server machines, and in the "network of networks" itself.