Earlier learning theory and algorithms were developed for an ideal world. Modern large-scale data sets and applications bring forth problems that must be addressed for learning to be effective, e.g., training points are often poorly labeled, the sample can be biased, the distributions may drift with time, and the sample points may not be i.i.d. This talk will address the specific problem of domain adaptation which arises when the distribution of the source labeled data somewhat differs from that of the target domain. It will present novel theoretical results for adaptation and provide algorithmic solutions derived from that theory. It will also report some preliminary experimental results. Joint work with Yishay Mansour and Afshin Rostamizadeh.