What are the roles of cadherins in epithelial mesenchymal transitions?
So let's just quickly define what cadherins are, using general information from wikipedia,

Source: Wikipedia
Cells express E-cadherin (epithelial), N-cadherin (neuronal, or P-cadherin (placental). These generally interact with ß-catenins to modulate cell adhesion. There are pathways intrinsic to cancer which downregulate the expression of cadherins,

Source: Epithelial–mesenchymal transition in development and cancer: role of phosphatidylinositol 3' kinase/AKT pathways
We see in the above pathway described in a study of PI3K/Akt signaling in cancer, some of the ways E-cadherin (encoded by CDH1) becomes downregulated. We also see that ß-catenin may be sequestered by E-cadherin at the plasma membrane, and cytosolic ß-catenin actually interacts within the nucleus as a transcription factor for SLUG (or snail2) where Snail2 is an essential mediator of Twist1-induced epithelial mesenchymal transition and metastasis. In the above figure this modulates reduced cell-cell adhesion, but we also see there's a number of other pathways which modulate the entirety of the EMT process.
What I found interesting, maybe unrelated
An interesting concept currently being investigated involves many of the shown membrane receptors, most of which are involved in some sort of crosstalk in aggressive cancer types. ROR1 was identified as a critical component for modulating EMT, and was shown to participate in Wnt signaling through it's frizzled domain, as well as crosstalk with Met tyrosine kinase, EGFR, and TGFß in some way. These interactions were able to increase expression of snail1/2, vimentin, etc. i.e. characteristics of EMT in breast adenocarcinoma (The linked article provides most of this background, but some may be missing, I'm unsure), and decrease expression of epithelial biomarkers like E-cadherin. When they used a ROR1 Ab to target ROR1, they found cadherin levels could be rescued, and morphological components returned to a more epithelial phenotype. Other articles showed this targeting could induce apoptosis in CLL and this occurs through interaction with PI3K/Akt.