Non-perturbative approaches in nanoscience are discussed. Traditional applications of these approaches cover description of charge transport and optical phenomena in nano-scale systems. We focus on finite-size effects in spin systems near the critical point, based on Monte Carlo (MC) method and some analytical arguments. We have performed MC simulations of the 3D Ising model for small, as well as large linear lattice sizes up to L = 2560, providing a numerical evidence for a recent challenging prediction, according to which the asymptotic decay of corrections to finite-size scaling is remarkably slower than it was expected before. Our approach along with several other non-perturbative approaches, like, e.g., the non-perturbative nonequilibrium Greens functions (NEGF) method, reveals a potential application of non-perturbative methods to nanoscience and nanotechnology through condensed matter physics, including semiconductor physics and physics of disordered systems like spin glasses.