  In high-energy hadronic collisions, hard parton scatterings with large
momentum transfers are prerequisites for the formation of hard and rare probes.
In heavy-ion collisions, these probes---final state particles related to the
early hard-parton scatterings---serve as a powerful tool to explore the whole
evolution of the medium including the quark--gluon plasma (QGP) stage. Hard
probes in proton-proton (pp) collisions test perturbative quantum
chromodynamics (pQCD) processes and hadronization, and provide a reference for
the nuclear collision systems. High-multiplicity pp collisions provide a bridge
to heavy-ion collisions, due to their large event activity.
  Heavy-flavor hadrons containing at least one charm or beauty quark belong to
the hard and rare probes. Recently, ALICE has measured a broad palette of
heavy-flavour baryons allowing to shed more light on charm fragmentation.
Measurements of charmonium production as a function of the event multiplicity
can provide insight into the interplay between charmonium-production processes
and soft processes driving the multiplicity. ALICE has investigated the
multiplicity dependence of J/$\psi$ production at midrapidity and the ratio of
$\psi \rm (2S)$ to J/$\psi$ yields at forward rapidity. The charm and beauty
cross sections can be constrained by fits of Monte-Carlo generators to the
measured dielectron continuum.
