The equation-free computational framework is an input-output approach to accelerating atomistic (MD, kMC, agent-based) computations. Short simulation bursts with an inner, "fine-scale" code are designed, executed, and their results processed to design new short fine scale computational experiments. Protocols for this "design of (computational) experiments" procedure are based on continuum numerical algorithms (integration, fixed point computation, bifurcation analysis etc.). I will illustrate the approach with two examples, involving the exploration of effective free energy surfaces of an MD and a kMC simulation respectively. A vital issue for the success of the approach is the identification of appropriate coarse-grained observables of the fine scale simulation. The use of diffusion maps (a data mining technique) to extract such observables from simulation data will be discussed. The work is in collaboration with several colleagues, including T. Frewen, G. Hummer and R. Coifman.