We shall introduce a class of attractors for 3-flows that encompasses the hyperbolic ones and the Lorenz attractor: they are transitive partially hyperbolic with central direction volume expanding and every equilibrium on it is hyperbolic.
Nowadays an element in this class is called either a singular-hyperbolic or a Lorenz-like attractor. We shall describe some relevant features of these attractors as (1) expansiveness, (2) existence of SRB measure, (3) exponential decay of correlations, (4) logarithm law for the hitting and recurrence time. We shall also discuss some extensions
of these results to n-dimensional homogeneous flows.