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The real-world data usually exhibits heterogeneous properties such as modalities, views, or resources, which brings some unique challenges wherein the key is Heterogeneous Representation Learning (HRL) termed in this paper. This brief survey covers the topic of HRL, centered around several major learning settings and real-world applications. First of all, from the mathematical perspective, we present a unified learning framework which is able to model most existing learning settings with the heterogeneous inputs. After that, we conduct a comprehensive discussion on the HRL framework by reviewing some selected learning problems along with the mathematics perspectives, including multi-view learning, heterogeneous transfer learning, Learning using privileged information and heterogeneous multi-task learning. For each learning task, we also discuss some applications under these learning problems and instantiates the terms in the mathematical framework. Finally, we highlight the challenges that are less-touched in HRL and present future research directions. To the best of our knowledge, there is no such framework to unify these heterogeneous problems, and this survey would benefit the community.