Several applications necessitate learning a very large number of parameters from small amounts of data, which can lead to overfitting, statistically unreliable answers, and large training/prediction costs. A common and effective method to avoid the above mentioned issues is to restrict the parameter-space using specific structural constraints such as sparsity or low rank. However, such simple constraints do not fully exploit the richer structure which is available in several applications and is present in the form of correlations, side information or higher order structure. Designing new structural constraints requires close collaboration between domain experts and machine learning practitioners. Similarly, developing efficient and principled algorithms to learn with such constraints requires further collaborations between experts in diverse areas such as statistics, optimization, approximation algorithms etc. This interplay has given rise to a vibrant area of "learning with structure in high dimensions". The goal of this workshop is to bring together the aforementioned diverse set of people who have worked in these areas and encourage discussions with an aim to help define the current frontiers for the area and initiate a discussion about meaningful and challenging problems that require attention.