The study of genorne rearrangement is much harder than the corresponding problems on DNA and protein sequences, because of the occurrences of numerous combinatorial structures. By explicitly exploring these combinatorial structures, the recently developed adequate subgraph theory shows that a family of these structures, adequate subgraphs, are informative in finding the optimal solutions to the rearrangement median problem. Its extension gives rise to the tree scoring method CASTS, which provides quick and accurate estimation of the number of rearrangement events, for any given topology. With a similar motivation, this paper discusses and provides solid but somewhat initial results, on combinatorial structures that are informative in phylogenetic inference. These structures, called rearrangement phylogenetic patterns, provide more insights than algorithmic approaches, and may provide statistical significance for inferred phylogenies and lead to efficient and robust phylogenetic inference methods on large sets of taxa.