Horizontal gene transfer (HGT) is believed to be ubiquitous among bacteria, and plays a major role in their genome diversification as well as their ability to develop resistance to antibiotics. In light of its evolutionary significance and implications in human health, developing accurate and efficient methods for detecting and reconstructing HGT is imperative. In this paper we provide a first likelihood framework for phylogeny-based HGT detection and reconstruction. Beside the formulation of various likelihood criteria, we offer novel hardness results and heuristics for efficient and accurate reconstruction of HGT under these criteria. We implemented our heuristics and used them to analyze biological as well as synthetic data. Our methods exhibited very good performance on the biological data, and preliminary results on the synthetic data show a similar trend. Further, preliminary results on synthetic data show good promise for detecting chimeric (partial) HGT, which has been mos...