Dermoscopy image analysis (DIA) is a growing field, with works being published every week. This makes it difficult not only to keep track of all the contributions, but also for new researchers to identify relevant information and new directions to be explored. Several surveys have been written in the past decade, but these tend to cover all of the steps of a CAD system, which can be overwhelming. Moreover, in these works, each of the steps is briefly discussed due to lack of space. Among the different blocks of the CAD system, the most relevant is the one devoted to feature extraction. This is also the block where existing works exhibit the most variability. Therefore, we believe that it is important to review the state-of-the-art on this matter. This work thoroughly explores the several types of features that have been used in DIA. A discussion on their relevance and limitations, as well as suggestions for future research are provided.