Understanding Domain Adaptation Learning - the good and the not so good

How can the learning of some target task benefit from training data generated by a different, yet related, task? In the past few years, a range of machine learning applications led to the development of various heuristic paradigms that address these domain adaptation and transfer learning issues. Such paradigms extend well beyond the scope of the currently available analysis. How should this a gap be addressed? I will survey some major algorithmic paradigms that have been proposed to address the transfer/adaptation learning and discuss the current theoretical understanding of these approaches. I also wish to touch upon what I view as useful vs not so insightful culture of research addressing this challenge.