Fluid viscous dampers (FVDs) are well-established supplemental energy dissipation devices that have been widely used for earthquake protection of structures. Optimal design, placement and sizing of FVDs have been extensively investigated in the last four decades. In this review paper, an overview of the most popular methodologies from the abundant literature in the field is presented. Key aspects and main characteristics of the different strategies to identify the optimal damping coefficients and the optimal placement of FVDs are scrutinized in a comparative manner. The optimal design problem is often solved through a numerical approach to a constrained optimization problem, by minimizing some performance criteria that are representative measures of the system response. With reference to two simple benchmark six-story shear-type structures subject to both a stochastic earthquake excitation and 44 natural ground motions extracted from the FEMA P695 record set, comparison of the seismic performance is carried out considering FVDs designed according to different methods — an overall number of 138 different design scenarios are incorporated in this comparative study. These methods are based either on a desired (target) damping ratio constraint or on a fixed total cost, here roughly related to the sum of the damping coefficients of the added FVDs. Some energy-based perspectives are also given in this review paper in order to interpret the seismic performance in terms of the amount of energy dissipated by the FVDs, out of the total input energy from the earthquake excitation. •A review of methodologies for the optimal design of FVDs is presented.•Key aspect and main characteristics of different strategies are outlined.•New energy-based perspectives for the optimal design of FVDs are proposed.•Extensive comparative study among different methodologies proposed in the literature.