  We describe some recent results on the dynamics of singular-hyperbolic (or
Lorenz-like) attractors: attractors in this class are expansive and so
sensitive with respect to initial data; they admit a unique physical measure
whose support is the whole attractor, which is hyperbolic and the equilibrium
state with respect to the center-unstable Jacobian; the hitting time associated
to a geometric Lorenz attractor satisfies a logarithm law; the rate of large
deviations for the physical measure on the ergodic basin of a geometric Lorenz
attractor is exponential.
