  We show the Cohen-Macaulayness and describe the canonical module of residual
intersections $J=\mathfrak{a}\colon_R I$ in a Cohen-Macaulay local ring $R$,
under sliding depth type hypotheses. For this purpose, we construct and study,
using a recent article of Hassanzadeh and the second named author, a family of
complexes that contains important informations on a residual intersection and
its canonical module. We also determine several invariants of residual
intersections as the graded canonical module, the Hilbert series, the
Castelnuovo-Mumford regularity and the type. Finally, whenever $I$ is strongly
Cohen-Macaulay, we show duality results for residual intersections that are
closely connected to results by Eisenbud and Ulrich. It establishes some tight
relations between the Hilbert series of some symmetric powers of
$I/\mathfrak{a}$. We also provide closed formulas for the types and for the
Bass numbers of some symmetric powers of $I/\mathfrak{a}.$
