Abstract: Fundamental groups of plane curve complements play an important role in the study of branched coverings. They may also be useful to distinguish the connected components of equisingular moduli spaces. The systematic study of these groups goes back to the 1930s with the founding works of O. Zariski and E. R. van Kampen. These works provide a powerful method to find a presentation of the fundamental group of the complement of any algebraic plane curve. In this talk, I will review Zariski-van Kampen's computation method and I will apply it to compute the fundamental groups of special classes of curves.