Exploration of the relationship between gene trees and their containing species trees leads to consideration of how to reconstruct species trees from gene trees and of the concept of phylogeny as a cloud of gene histories. When gene copies are sampled from various species, the gene tree relating these copies might disagree with the species phylogeny. This discord can arise from horizontal transfer (including hybridization), lineage sorting, and gene duplication and extinction. Lineage sorting could also be called deep coalescence, the failure of ancestral copies to coalesce (looking backwards in time) into a common ancestral copy until deeper than previous speciation events. These events depend on various factors; for instance, deep coalescence is more likely if the branches of the species tree are short (in generations) and wide (in population size). A similar dependence on process is found in historical biogeography and host-parasite relationships. Each of the processes of discord could yield a different parsimony criterion for reconstructing the species tree from a set of gene trees: with horizontal transfer, choose the species tree that minimizes the number of transfer events; with deep coalescence, choose the tree minimizing the number of extra gene lineages that had to coexist along species lineages; with gene duplication, choose the tree minimizing duplication and/or extinction events. Maximum likelihood methods for reconstructing the species tree are also possible because coalescence theory provides the probability that a particular gene tree would occur given a species tree (with branch lengths and widths specified). In considering these issues, one is provoked to reconsider precisely what is phylogeny. Perhaps it is misleading to view some gene trees as agreeing and other gene trees as disagreeing with the species tree; rather, all of the gene trees are part of the species tree, which can be visualized like a fuzzy statistical distribution, a cloud of gene histories. Alternatively, phylogeny might be (and has been) viewed not as a history of what happened, genetically, but as a history of what could have happened, i.e., a history of changes in the probabilities of inter-breeding.