We introduce and study a class of free boundary models with nonlocal diffusion. We show that this nonlocal problem has a unique solution defined for all time, and then examine its long-time dynamical behavior when the growth function is of Fisher-KPP type. We prove that a spreading-vanishing dichotomy holds, though for the spreading-vanishing criteria significant differences arise from the well known local diffusion model. Finally, as applications, we consider the dynamics of the nonlocal epidemic model, the nonlocal L-V predator-prey model and the nonlocal L-V competition model with free boundaries. This talk is based on joint works with Jia-Feng Cao (LUT), Yihong Du (UNE), Fang Li (SYU), Lei Li (HUT), Wenjie Ni (UNE), Mingxin Wang (HPU & HIT) and Meng Zhao (NWNU).