An important property of a dynamical system is its reactivity, i.e., the initial rate of growth of the norm of the state vector. However, most literature on reactivity has focused on continuous time systems. Here we define the reactivity of discrete time systems and apply it to characterize the dynamics of network systems and Markov chains. We also introduce the concept of reactability, which measures the ability of a system to be made reactive, under the condition that the system is stable. We identify properties of a system that provide minimal reactability. Then we formulate and solve an optimization problem that perturbs an existing discrete time system to make it minimally reactable.