Domain adaptation is a fundamental learning problem where one wishes to use labeled data from one or several source domains to learn a hypothesis performing well on a different, yet related, domain for which no labeled data is available. This generalization across domains is a very significant challenge for many machine learning applications and arises in a variety of natural settings, including NLP tasks (document classification, sentiment analysis, etc.), speech recognition (speakers and noise or environment adaptation) and face recognition (different lighting conditions, different population composition). The learning theory community has only recently started to analyze domain adaptation problems. In the talk, I will overview some recent theoretical models and results regarding domain adaptation. This talk is based on joint works with Mehryar Mohri and Afshin Rostamizadeh.