In this paper new non-linear predator-prey models with dormant predators and chemotaxis are proposed and studied. In the first model, chemotaxis is considered to affect the behavior of active predators so that they try to move towards the regions where the density of dormant predators is higher. In the second model, a similar chemotactic effect is assumed to affect also the behavior of preys. For both systems, uniform boundedness and global existence of solutions are proved by means of the Moser-Alikakos iterative method and the uniform asymptotic behavior of the solutions is analyzed for the constant stationary states in order to understand their time and spatial dynamics. Further, using a Generalized Finite Difference Method (GFDM) we confirm that the properties of the continuous model are also preserved for the resulting discrete model.