Photonic integrated circuits (PICs) have attracted great attention as promising platforms for high-data-rate communications and high-performance computing. For the PICs, photonic devices with compatible materials, compact footprint, high-performance, and sophisticated functionalities are necessary building blocks. Design optimization to implement such devices for target applications and requirements are of critical importance. In this respect, inverse design methods, including iterative optimizations and deep neural networks, have demonstrated significant advantages over the traditional simulation-based trial-and-error optimization approach. We provide an overview of the recent progress on the inverse designs for the integrated photonic devices. The principles and procedure of the inverse design methods are presented and discussed, followed by a summary of the methods employed for specific integrated photonic devices in different integrated photonics material platforms. Finally, topics of future applications and fabrication constraints for the inverse design methods are discussed.