The prediction and interpretation of conformational properties of branched
polymers is difficult, due to the complexity and variety of these structure
s. Numerical simulations are, consequently, very useful in the investigatio
n of these systems. This review describes the application of numerical simu
lation techniques to relevant theoretical problems concerning branched poly
mer systems, taking also into account the related experimental data. Monte
Carlo, Molecular Dynamics and Brownian Dynamics methods are employed to sim
ulate the equilibrium and dynamic behavior, and also to reproduce hydrodyna
mic properties. The simulations are performed on several polymer models. Th
us, different Monte Carlo algorithms have been devised for lattice and off-
lattice models. Moreover Molecular Dynamics and Brownian Dynamics can be ca
rried out for detailed atomic or coarse-grained chains. A great amount of i
nvestigation has been engaged in the understanding of uniform homopolymer s
tars as single chains, or in non-diluted solutions and melts, employing thi
s variety of techniques, models and properties. However, other important st
ructures, such as stars with different types of monomer units, combs, brush
es, dendrimers and absorbed branched polymers have also been the subject of
specific simulation studies.