For some time, it has become apparent that many evolving entities (genes, cells, viruses, plasmids, genomes, etc.) are mosaic. That is to say, we cannot describe their evolutionary history without telling more than one story about it. Genes can be chimaeric and indeed, it is arguable that it is almost impossible for them not to be chimaeric, if you go far enough back in time. This means that we need to describe the evolutionary history of evolving units by using diagrams or ideas that can accept and incorporate mosaic history.
The whole area of phylogenetic network analysis has been in existence for at least three decades (depending on how you wish to define this field, you might feel it has existed for hundreds of years). In fact, there is a superb review of the whole area in GBE from less than two years ago  that details all the different kinds of networks, how to construct them and what they mean.
However, this kind of analysis will only allow us to see network-likeness in a restricted kind of datum. We can construct these kinds of networks either when we have recombination within an alignment of homologous sequences or when we have a collection of trees that manifest topological differences because they have different histories. Using these approaches, we can identify hybrid organisms or recombined homologous entities.
What about the broader scope of evolving entities? What about when a gene X fuses with a different gene Y? How do we analyse the three related entities in this case? You have the unfused family X, the unfused family Y and the fused family XY. Can we make a single alignment? Do we have a structure that we can use in order to understand their evolution? What do we do when it gets more complicated than this simple toy scenario?
What about microbial consortia? Or the dependence of a phage on a bacterium and vice versa? These organisms depend on one another for/during their evolutionary history.
Nobody would dream of writing an evolutionary biology textbook these days without including in that textbook some chapter on kin selection – we feel that our picture of evolution is incomplete without such a chapter. So, why do we have a picture of life on this planet that rarely, if ever, mentions mosaic structures. If they are mentioned, then they are usually mentioned in the narrow light of simply dealing with homologous recombination or perhaps hybridization between things of the same level – chromosomes or genomes or species.
Today PNAS published a manuscript  where, along with some distinguished co-authors, we set out the case for including mosaic entities more centrally in our discussions of things like the Tree of Life Hypothesis. The paper describes mosaic entities: some familiar and some not-so-familiar. We ask the reader to think about what we might know if we focussed on trying to understand these entities in an evolutionary framework.
I think there is a lot of biology, computer science and mathematics to be done in our efforts to understand these entities and I think there is a proper programme of research in this area. I also feel that in 10 years time we might look back on many of our evolutionary analyses and feel that they were somewhat naiive because they left out the analysis of mosaic entities.
 Huson, D. H., & Scornavacca, C. (2011). A survey of combinatorial methods for phylogenetic networks. Genome Biology and Evolution, 3, 23–35. doi:10.1093/gbe/evq077
 Bapteste, E., Lopez, P., Bouchard, F., Baquero, F., McInerney, J. O., & Burian, R. M. (n.d.). Evolutionary analyses of non-genealogical bonds produced by introgressive descent.