As mentioned in the introduction domain adaptation is a relatively new field. It is also relatively loosely defined with regards to e.g. how 'related' are the domains, and how 'few' labelled samples exist in the target domain. Also, the general problem statement applies to several application domains, such as natural language processing and computer vision. For all these reasons, there is a big variety in the proposed methods. Inspired by the categorization proposed in [Jiang, 2008], we begin by considering instance weighting methods for relaxation of the DA assumptions in Sec. 3. We consider methods utilizing the source **data** to regularize target models in Sec. 4. We then survey method seeking common representation across domains in Sec. 5. Section 6 make connections to transfer learning, and Sec. 7 briefly survey method for multi-modal learning.