Parametric identification of viscous damping models in the context of linear vibration theory is studied. Frequency domain identification methods based on measured frequency response functions (FRFs) are considered. Existing methods are classified into two main groups: matrix methods which use directly the measured FRF matrix, and modal methods which use modal parameters deduced from the FRFs. A new group of methods called enhanced methods is introduced to improve the performance of the matrix methods. These three groups of identification methods are critically reviewed and a systematic simulation study is then conducted to compare their performance. Four simulation examples are presented to bring out the relative merits of the identification methods. The success of each method is evaluated with reference to four norms introduced. Robust methods of identification are identified.