  Phylogeny is the study of the relations between biological entities. From it,
the need to compare tree-like graphs has risen and several metrics were
established and researched, but since there is no definitive way to compare
them, its discussion is still open nowadays. All of them emphasize different
features of the structures and, of course, the efficiency of these computations
also varies. The work in this article is mainly expositive (a lifting from a
collection of papers and articles) with special care in its presentation
(trying to mathematically formalize what was not presented that way previously)
and filling (with original work) where information was not available (or at
least, to our knowledge) given the frame we set to fit these metrics, which was
to state their discriminative power and time complexity. The Robinson Foulds,
Robinson Foulds Length, Quartet, Triplet, Triplet Length, Geodesic metrics are
approached with greater detail (stating also some of its problems in
formulation and discussing its intricacies) but the reader can also expect that
less used (but not necessarily less important or less promising) metrics will
be covered, which are Maximum Aggreement Subtree, Align, Cophenetic Correlation
Coeficcient, Node, Similarity Based on Probability, Hybridization Number and
Subtree Prune and Regraft. Finally, some challenges that sprouted from making
this synopsys are presented as a possible subject of study and research.
