  Spin glasses are the paradigm of complex systems. These materials present
really slow dynamics. However, the nature of the spin glass phase in finite
dimensional systems is still controversial. Different theories describing the
low temperature phase have been proposed: droplet, replica symmetry breaking
and chaotic pairs. We present analytical studies of critical properties of spin
glasses, in particular, critical exponents at and below the phase transition,
existence of a phase transition in a magnetic field, computation of the lower
critical dimension (in presence/absence of a magnetic field). We also introduce
some rigorous results based on the concept of metastate. Finally, we report
some numerical results regarding the construction of the Aizenman-Wehr
metastate, scaling of the correlation functions in the spin glass phase and
existence of a phase transition in a field, confronting these results with the
predictions of different theories.
