Over the past decades, classical optimization methods, including gradient-based topology optimization and the evolutionary algorithm, have been widely employed for the inverse design of various photonic structures and devices, while very recently neural networks have emerged as one powerful tool for the same purpose. Although these techniques have demonstrated their superiority to some extent compared to the conventional numerical simulations, each of them still has its own imitations. To fully exploit the potential of intelligent optical design, researchers have proposed to integrate optimization methods with neural networks, so that they can work coordinately to further boost the efficiency, accuracy and capability for more complicated design tasks. In this mini-review, we will highlight some representative examples of the hybrid models to show their working principles and unique proprieties. • This review article focuses on the hybrid models that combines neural networks with other classical optimization algorithms for photonic design. • It provides specific examples of different types of hybrid models, and discusses their unique advantages for improving the performances of the design models and photonic devices. • It provides adequate information about the recent progress, and motivate researchers with diverse backgrounds to contribute to this emergent field.