Measurements of open heavy-flavour production in p--Pb collisions allow assessing the Cold Nuclear Matter effects due to the presence of a nucleus in the colliding system. Moreover, the study of a modification of the heavy-flavour hadrons transverse momentum in high-multiplicity p--Pb collisions can give insight into the possible presence of collective effects also in small systems.
In this report, the ALICE measurements on open heavy-flavour production in p--Pb collisions at
$\sqrt{s_{\rm{NN}}}$ = 5.02 and 8.16~TeV are presented. Emphasis is given to measurements in high-multiplicity p--Pb collisions and to the recent elliptic flow measurements of leptons from heavy-flavour decay hadrons.