  We studied the statics and dynamics of elastic manifolds in disordered media
with long-range correlated disorder using functional renormalization group
(FRG). We identified different universality classes and computed the critical
exponents and universal amplitudes describing geometric and velocity-force
characteristics. In contrast to uncorrelated disorder, the statistical tilt
symmetry is broken resulting in a nontrivial response to a transverse tilting
force. For instance, the vortex lattice in disordered superconductors shows a
new glass phase whose properties interpolate between those of the Bragg and
Bose glasses formed by pointlike and columnar disorder, respectively. Whereas
there is no response in the Bose glass phase (transverse Meissner effect), the
standard linear response expected in the Bragg-glass gets modified to a power
law response in the presence of disorder correlations. We also studied the long
distance properties of the O(N) spin system with random fields and random
anisotropies correlated as 1/x^{d-sigma}. Using FRG we obtained the phase
diagram in (d,sigma,N)-parameter space and computed the corresponding critical
exponents. We found that below the lower critical dimension 4+sigma, there can
exist two different types of quasi-long-range-order with zero order-parameter
but infinite correlation length.
