The tree of zeta functions has many branches including those from number theory (Riemann and Dedekind zeta functions), spectral geometry of manifolds (Selberg's zeta function), and graph theory (Ihara's zeta function). Applications include analogues of the prime number theorem and analogues of the work on what is now called quantum chaos - the statistics of energy levels of various non-classical physical systems. For example, the poles of the Ihara zeta function of a connected regular graph satisfy the Riemann hypothesis if and only if the graph is a Ramanujan graph (meaning that the second largest eigenvalue of the adjacency matrix, in absolute value, is in some sense smallest possible). In this talk I will compare the various sorts of zetas and investigate properties and applications of 3 types of graph zeta functions (the vertex or Ihara zeta, the edge and the path zetas) considered in Stark and Terras, Advances in Math., Vol. 121 (1996) and Vol. 154 (2000).