Important efforts have been dedicated in the past few years to describe
near-barrier heavy-ion collisions with microscopic quantum theories like the
time-dependent Hartree-Fock approach and some of its extensions. However, this
field is still facing important challenges such as the description of cluster
dynamics, the prediction of fragment characteristics in damped collisions, and
sub-barrier fusion by quantum tunnelling. These challenges are discussed and
possible approaches to solve them are presented.Comment: 13 pages, 4 figures. To appear in the special issue of Journal of
Physics G on open problems in nuclear reaction theor
