Many massive graphs (such as WWW graphs and Call graphs) share certain universal characteristics which can be described by the so-called the “power law”. In this paper, we first briefly survey the history and previous work on power law graphs. Then we give four evolution models for generating power law graphs by adding one node/edge at a time. We show that for any given edge density and desired distributions for in-degrees and out-degrees (not necessarily the same, but adhered to certain general conditions), the resulting graph almost surely satisfy the power law and the in/out-degree conditions. We show that our most general directed and undirected models include nearly all known models as special cases. In addition, we consider another crucial aspect of massive graphs that is called “scale-free” in the sense that the frequency of sampling (w.r.t. the growth rate) is independent of the parameter of the resulting power law graphs. We show that our evolution models generate scale-free power law graphs.