Abstract This paper provides a topical review of work on systems based on magnetic nanostructured thin films on polymer substrates. This topic has indeed experienced a significant growth in the last ten years. Several studies show a strong potential of these systems for a number of applications requiring functionalities on non-planar surfaces. However, the deformations necessary for this type of applications are likely to modify their magnetic properties, and the relationships between strain fields, potential damages and functional properties must be well understood. This review focuses both on the development of techniques dedicated to this research, on the synthesis of the experimental results obtained over the last ten years and on the perspectives related to stretchable or flexible magnetoelectric systems. In particular, the article focuses on the links between magnetic behavior and the strain field developing during the whole history of these systems (elaboration, reversible and irreversible loading).