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The field of materials science has witnessed a transformative shift with the advent of representation learning techniques, particularly for analyzing complex microstructures. This review synthesizes recent conceptual advances in representation learning, including deep neural networks, autoencoders, and vision transformers, applied to microstructure data for tasks such as property prediction, inverse design, and evolution modeling. We explore how these methods extract latent features from high-dimensional microstructure images, enabling efficient computation and discovery of structure-property relationships. However, interpretability remains a significant challenge, as black-box models often obscure the physical meaning of learned representations, hindering trust and scientific insight. We discuss strategies for enhancing interpretability, such as attention mechanisms, heat maps, and post-hoc explanations, drawing from recent studies in alloy microstructures and additive manufacturing. The review highlights the integration of domain knowledge to disentangle representations and address data scarcity issues. By examining case studies in metals, ceramics, and composites, we identify gaps in current approaches, including bias in learned features and limited generalizability across materials classes. Ultimately, this review aims to guide future research toward interpretable representation-learning frameworks that accelerate materials design and foster a deeper understanding of microstructural phenomena.