Spin Torque Oscillators (STO) are nano-sized Radio-Frequency oscillators whose frequency agility can be tuned by an order of magnitude. This tuning originates from the non-linear properties of the underlying magnetization dynamics that is induced by spin transfer torque (STT) in multilayered magnetic nanostructures. Being highly tunable in frequency has the inconvenient of creating a very strong sensitivity to noise. As a result the spectral purity of STOs is far below the one required for applications for instance in telecommunications. The magnetization dynamics induced by STT has been described theoretically in the frame of nonlinear spin wave theory that makes the essential features of the underlying properties very transparent. However important information on the excitation mode are "buried" in phenomenological parameters such as NU the amplitude-phase coupling and Gp the amplitude relaxation rate. Determining these parameters with accuracy from experiments is thus an important issue. This thesis describes several experimental methods to extract these parameters. The first is time domain noise spectroscopy which permits to extract phase and amplitude noise Power Spectral Densities. Their analysis in the frame of theoretical models allows direct extraction of the nonlinear parameters, but also to quantify the technological relevant phase noise. This is demonstrated for magnetic tunnel junction devices. A second method is the analysis of higher harmonics linewidth, where it is shown that due to the non-isochronous property of STOs, the relationship between Dfn and Df1 is non-trivial and allows to extract NU and Gp. We then apply the information gathered on the autonomous dynamics of STOs to understand the non-autonomous dynamics of STOs that are a prerequisite for the use of STOs in complex RF architectures. It is shown experimentally how the nonlinear parameters influence this non-autonomous behaviour.