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Spectral unmixing is one of the most important quantitative analysis tasks in hyperspectral data processing. Conventional physics-based models are characterized by clear interpretation. However they may not be suitable for analyzing scenes with unknown complex physical characteristics. Data-driven methods have developed rapidly in recent years, in particular deep learning methods because they possess superior capability in modeling complex and nonlinear systems. Simply transferring these methods as black-boxes to conduct unmixing may lead to low physical interpretability and generalization ability. This article reviews hyperspectral unmixing works that integrate advantages of both physics-based models and data-driven methods by means of deep neural network structures design, prior design and loss design. Most of these methods derive from a common mathematical optimization framework, and combine good interpretability with high accuracy.