The nature of the low temperature phase of short-range spin glasses is still a controversial issue, which has recently attracted renewed interest. Two very different pictures have been extensively discussed: the droplet model and the replica  symmetry breaking theory. In this talk, I will review our recent investigations of the low temperature phase of short-range Ising spin glasses. I will present the results of an approach based on studying the response of the ground state to an external perturbation, using efficient ground state algorithms, as well as the results of Monte Carlo simulations at very low temperatures. I will compare our results with several theoretical scenarios: the droplet model, the replica symmetry breaking theory, and a new intermediate scenario in which there are large scale excitations which cost a finite energy in the thermodynamic limit, but whose surface has a vanishing density.

References available at http://mozart.ucsc.edu/matteo