  Since its discovery in 1938, superfluidity has been the subject of much
investigation because it provides a unique example of a macroscopic
manifestation of quantum mechanics. About 60 years later, scientists
successfully observed this phenomenon in the microscopic world though the
spectroscopic Andronikashvili experiment in helium nano-droplets. This
reduction of scale suggests that not only helium but also para-H2 (pH2) can be
a candidate for superfluidity. This expectation is based on the fact that the
smaller number of neighbours and surface effects of a finite-size cluster may
hinder solidification and promote a liquid-like phase. The first prediction of
superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo
simulations. The possible superfluidity of pH2 was later indirectly observed in
a spectroscopic Andronikashvili experiment in 2000. Since then, a growing
number of studies have appeared, and theoretical simulations have been playing
a special role because they help guide and interpret experiments. In this
review, we go over the theoretical studies of pH2 superfluid clusters since the
experiment of 2000. We provide a historical perspective and introduce the basic
theoretical formalism along with key experimental advances. We then present
illustrative results of the theoretical studies and comment on the possible
future developments in the field. We include sufficient theoretical details
such that the review can serve as a guide for newcomers to the field.
