The field of numerical homogenization concerns the numerical approximation of the solution space of, for example, divergence form elliptic equation with $L^\infty$ coefficients by a finite-dimensional space. Numerical homogenization methods such as MsFEM and HMM are developed from classical homogenization concepts such as periodic homogenization and scale separation. For problems with nonseparable scales, significant progress has been achieved in the recent decades. In particular, the transfer property is introduced, and the optimal convergence rate is identified in by Berlyand and Owhadi. Then the focus becomes the so-called “localization problem”, namely, how to construct a finite-dimensional space with optimal convergence rate and optimally localized bases. The so-call Rough Polyharmonic Splines (RPS) with optimal approximation and localization properties is developed by Berlyand and collaborators. Those ground-breaking contributions open avenues for recent developments such as Bayesian/game theoretical approach to numerical analysis, as well as low-rank approximation of elliptic boundary value problems with high-contrast coefficients.