  The production of open heavy-flavour particles was studied in p-Pb collisions
at $\sqrt{s_\mathrm{NN}}=5.02$ TeV using the ALICE detector. Three separate
observables were used: the hadronic decays of D mesons at mid-rapidity, and
semileptonic decays of heavy-flavour hadrons to electrons and muons at
mid-rapidity and forward rapidity, respectively. The most recent ALICE
measurements of the nuclear modification factor, $R_\mathrm{pPb}$, of open
charm and beauty are reported, along with the centrality and multiplicity
dependence of D-meson production in p-Pb collisions.
