• We review current knowledge about the biology of the genus Acacia, and Acacia dealbata Link (silver wattle) in particular, as an invader in Europe, focusing on (i) the biology of the genus Acacia; (ii) biological attributes that are important for the invasiveness of the genus and A. dealbata; (iii) possible hypotheses for the invasion success; and (iv) control methods.• Several Australian wattles have been recorded as naturalized in Europe. Acacia has attained pest proportions in certain habitats and protected sites (notably coastal dunes, river courses, natural parks and biosphere reserves).• The spread of Acacia dealbata seems to be assisted by human interference such as soil disturbance and severe fires. The biological attributes favoring invasion by A. dealbata include tolerance of changing soil conditions, the ability to take advantage of environmental disturbance, phenotypic plasticity, vegetative reproduction, fire tolerance and allelopathic potential.• Different hypotheses explaining invasiveness and transition between invasion steps related to biological attributes as the key factor for A. dealbata invasion are discussed. Effects on the biodiversity of native flora are little understood and studies of suppression of autochthonous species are needed. It is desirable that further studies comparing Acacia at field sites in their native and exotic range should be done.• Understanding the biology of invasive wattles in Europe is the first step to an effective control method. Studies comparing plant invaders at field sites in their native and invaded areas seem to be most appropriate in order to be able to attack the most vulnerable stages.