Many complex systems such as biological and social systems can be modeled using graph structures called biological networks and social networks. Instead of studying separately each of the elements composing such complex systems, it is easier to study the networks representing the interactions between the elements of these systems. A commonly known fact in biological and social networks’ analysis is that in most networks some important or influential elements (e.g. essential proteins in PPI networks) are placed in some particular positions in a network. These positions (i.e. vertices) have some particular structural properties. Centrality measures quantify such facts from different points of view. Based on centrality measures the graph elements such as vertices and edges can be ranked from different points of view. Top ranked elements in the graph are supposed to play an important role in the network. This paper presents a comprehensive review of existing different centrality measures and their applications in some biological networks such as Protein-Protein interaction network, residue interaction and gene–gene interaction networks.