After presenting the main notions and results about
congruences of k-planes, we dwell upon congruences of lines,
mainly of order one. We survey the classification results in the
projective spaces of dimension 3 and 4, which are almost complete,
and the (partial) results and some conjectures in higher
dimension. Finally we present some new results, in particular a
degree bound for varieties with one apparent double point, a new
class of examples with focal locus of high degree, and some general
results about the classification of first order congruences of
lines in $\mathbb P^4$ with reducible focal surface.
