Most standard cluster interconnect technologies are flexible with respect to network topology. This has spawned a substantial amount of research on topology-agnostic routing algorithms, which make no assumption about the network structure, thus providing the flexibility needed to route on irregular networks. Actually, such an irregularity should be often interpreted as minor modifications of some regular interconnection pattern, such as those induced by faults. In fact, topology-agnostic routing algorithms are also becoming increasingly useful for networks on chip (NoCs), where faults may make the preferred 2D mesh topology irregular. Existing topology-agnostic routing algorithms were developed for varying purposes, giving them different and not always comparable properties. Details are scattered among many papers, each with distinct conditions, making comparison difficult. This paper presents a comprehensive overview of the known topology-agnostic routing algorithms. We classify these algorithms by their most important properties, and evaluate them consistently. This provides significant insight into the algorithms and their appropriateness for different on- and off-chip environments.