Following the work on homeotic mutants by Ed Lewis, the phenomenology of homeosis in animals was further elaborated by discovery of a conserved DNA binding sequence present in many  homeotic proteins. 
Thus, the 60 amino acid DNA binding protein domain was named the homeodomain, while the 180 bp nucleotide sequence encoding it was named the homeobox. The homeobox gene clusters studied by Ed Lewis were named the Hox genes, although many more homeobox genes are encoded by animal genomes than those in the Hox gene clusters.
The homeotic-function of certain proteins was first postulated to be that of a "selector" as proposed by Antonio Garcia-Bellido. 
By definition selectors were imagined to be (transcription factor) proteins that stably determined one of two possible cell fates for a cell and its cellular descendants in a tissue.   
While most animal homeotic functions are associated with homeobox-containing factors, not all homeotic proteins in animals are encoded by homeobox genes, and further not all homeobox genes are necessarily associated with homeotic functions or (mutant) phenotypes.
The concept of homeotic selectors was further elaborated or at least qualified by Michael Akam in a so-called "post-selector gene" model that incorporated additional findings and "walked back" the "orthodoxy" of selector-dependent stable binary switches.
The concept of tissue compartments is deeply intertwined with the selector model of homeosis because the selector-mediated maintenance of cell fate can be restricted into different organizational units of an animal's body plan.
In this context, newer insights into homeotic mechanisms were found by Albert Erives and colleagues by focusing on enhancer DNAs that are co-targeted by homeotic selectors and different combinations of developmental signals.
This work identifies a protein biochemical difference between the transcription factors that function as homeotic selectors versus the transcription factors that function as effectors of developmental signaling pathways, such as the Notch signaling pathway and the BMP signaling pathway.
This work proposes that homeotic selectors function to "license" enhancer DNAs in a restricted tissue compartment so that the enhancers are enabled to read-out developmental signals, which are then integrated via polyglutamine-mediated aggregation.