The research on nanophotonic devices has made great progress during the past decades. It is the unremitting pursuit of researchers that realize various device functions to meet practical applications. However, most of the traditional methods rely on human experience and physical inspiration for structural design and parameter optimization, which usually require a lot of resources, and the performance of the designed device is limited. Intelligent algorithms, which are composed of rich optimized algorithms, show a vigorous development trend in the field of nanophotonic devices in recent years. The design of nanophotonic devices by intelligent algorithms can break the restrictions of traditional methods and predict novel configurations, which is universal and efficient for different materials, different structures, different modes, different wavelengths, etc. In this review, intelligent algorithms for designing nanophotonic devices are introduced from their concepts to their applications, including deep learning methods, the gradient-based inverse design method, swarm intelligence algorithms, individual inspired algorithms, and some other algorithms. The design principle based on intelligent algorithms and the design of typical new nanophotonic devices are reviewed. Intelligent algorithms can play an important role in designing complex functions and improving the performances of nanophotonic devices, which provide new avenues for the realization of photonic chips.