We describe the reasons why the newly recognized process of horizontal gene transfer (HGT) forces evolutionists who study classification and microbiology to go beyond the classical Darwinian framework. We recall the importance of processes in philosophical definitions of species and for taxonomical purposes in general. More precisely, we present a brief description of a possible transition from a thinking inspired by essentialism to eliminative pluralism in the species debate and we insist on a major philosophical lesson: that processes matter and that, consequently, HGT cannot be overlooked in microbial classification. We then expand the conclusions of eliminative pluralism to microbial classification, namely (i) that species are not real and (ii) that overlapping taxonomies are equally legitimate when they are based on real natural processes. We introduce alternatives to the traditional species concept and describe what we call evolutionary units. Two types of units can be described: coherent and composite. The former are sets of co-evolving genes, pathways, or organisms, which share the same phylogenetic origin, while the latter comprise genes, pathways, or organisms with component parts from multiple phylogenetic origins. These evolutionary units are either "mostly flexible" or "mostly rigid" in their genetic composition and we discuss how this dissimilarity could profoundly affect our systematics practice. In this chapter, we illustrate how much there is to learn from the reconstruction of the complex evolutionary histories of all evolutionary units - large or small - by giving up the notion of species for recombining microbes, and suggest replacing a unique nested hierarchy of life with a comprehensive database including overlapping taxonomical groups.