  Hadron production in hard scattering reactions is described by the
hadronization mechanism which combines quarks into final-state hadrons. Within
the theoretical framework of leading-twist collinear QCD, the cross section for
hadron production in semi-inclusive deep-inelastic scattering can be factorized
into a hard scattering cross section describing the hard interaction at the
quark level calculable in perturbative QED, and non-perturbative universal
functions: parton distribution functions which reflect the quark structure of
initial-state hadrons and collinear fragmentation functions which encode
details on the hadronization process. In the last decades, a major effort has
been achieved on theoretical and experimental levels and allowed to constraint,
with very high precision, parton distribution functions except strange quark
distribution, which still carries large uncertainties. Fragmentation functions,
however, remain at a very preliminary stage of study with a growing interest in
a more accurate and precise knowledge. Nowadays, while pion fragmentation
functions are known with a limited precision and kaon fragmentation functions
are poorly known, the situation for dihadron fragmentation functions turns out
to be behind the schedule and no studies or measurements have been yet
performed.Measuring both single hadron and hadron pair multiplicities in
semi-inclusive deep inelastic scattering at COMPASS represent a fundamental
contribution towards a better understanding of the hadronization process and a
first measurement for hadron pair multiplicities in SIDIS. These measurements
will be presented and discussed.
