In this talk, I will report our recent research on the global dynamics of a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories  of asymptotically autonomous and periodic semiflows, we establish the threshold type results on the long-time behavior of solutions for such a system in the cases of  asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and super-solutions, and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of Dengue fever transmission to study the effect of time-varying domain on the basic reproduction number.