Glassy dynamics is one of the major open problems in Condensed Matter Physics, and it has a deep impact on many disciplines, from the myriad engineering applications of amorphous materials, to its role in the preservation of living organisms in their dormant state. The dramatic slowdown of relaxation in the glassy state causes materials to fall out of equilibrium. This has striking consequences, including "aging," i.e. the breakdown of time translation invariance (the system always "remembers" how long it has been since it was quenched below the glass transition temperature); and also the breakdown of the "Fluctuation-Dissipation Theorem" connecting spontaneous fluctuations (noise) with the response to an applied field. Recent experiments have started to probe glassy materials at distance scales of the order of tens of nanometers, and uncovered direct evidence for the presence of heterogeneities in the dynamics, which have not been understood in the framework of traditional mean field theories. In this talk I will present a new theoretical framework that goes beyond mean field theory and is capable of describing the heterogeneous character of the dynamics in spin glasses. I will discuss some of the following questions: what is the mechanism for the presence of heterogeneities in the glassy state? can the fluctuations at different times be connected in a simple way? is it possible to obtain a new relationship between noise and response, that applies to experiments probing nanoscale-size regions?