Composite materials are heterogeneous in nature and suffer from complex non-linear modes of failure, such as delamination, matrix crack, fiber-breakage, and voids, among others. The early detection of damage in composite structures, such as airplanes, is imperative to avoid catastrophic failure and tragic consequences. This paper reports on the use of machine learning techniques for the damage assessment (i.e., detection, quantification, and localization) of smart composite structures. The success of the machine learning paradigm for damage assessment depends on the representational capability of the discriminative features for the problems of interest. However, from a practical standpoint, it is not possible to define a global or superset of discriminative features that could discriminate between damaged and undamaged states of the structures, and simultaneously make a distinction between various modes of failures. In addition, one machine learning algorithm may show optimum performance for the discriminative features of a particular problem but fails for others. This article focuses on a review of discriminative features and the corresponding machine learning algorithms (both supervised and unsupervised), for various types of damage in smart composite structures.