Horizontal gene transfer (HGT) between bacterial species is a source of genome evolution and biodiversity. The most frequent HGT process involves cell-to-cell contacts (conjugation). Initiation of conjugative DNA transfer requires the action of a protein, named relaxase. In the receptor cell, the incoming DNA is inherited either by replication (plasmids) and/or integration into the host chromosome (genomic islands). HGT may represent an evolutionary success for the recipients if the newly acquired genetic trait does not affect their fitness. HGT may contribute to bacterial adaptation and fruitful colonization of new niches. We study the mechanisms involved in the initiation of conjugative transfer in Gram-positive bacteria, with emphasis in streptococci and enterococci, mediated by plasmids or by Integrative and Mobilizable Elements (IMEs). Our work combines genetic, biochemical, and biophysical approaches to acquire a comprehensive interpretation of the HGT in these bacteria.