<Abstract> 

Evolving nanotechnologies and further understanding of nanophotonics have recently enabled the control of electromagnetic waves using metasurfaces. Since metasurfaces can provide diverse optical characteristics depending on their geometries, the forward design of metasurfaces conventionally has been employed through an understanding of the physical effects of each geometrical parameter. In contrast, the inverse design approach optimizes the metasurface geometry using computational algorithms. This review discusses recent studies on constructing generative models for the inverse design of nanophotonic metasurfaces. The generative model for inverse design is constructed mainly with three components: an evaluator, a generator, and a criterion. The evaluator, which can be implemented by physical simulators or deep neural networks, determines whether the input metasurface geometry satisfies the target optical characteristics. The generator suggests new possible design candidates that may have optical properties close to the target. The criterion, which includes algorithms based on mathematical optimization and artificial intelligence, manages the operation of a generative model while satisfying the convergence of optimal solutions. Inverse design takes advantage of larger design space for customized applications along with the possibility of investigating new physics, and hence it is expected to improve metasurfaces further with the emerging computational algorithms.