Practical notes on unbalance, misalignment, excessive radial loads, fluid-induced vibrations, frictional excitations, and torsional-lateral coupled vibrations in turbomachines are discussed. Advanced vibrational condition monitoring methods are presented which can be used for identification of these malfunctions. The effects of the anisotropic supports, asymmetric rotor assemblies, bearings and couplings on rotordynamics of turbomachines are described. Case studies are also presented. The damped unbalance dynamic response test (known as the “synchronous test”) consists of inputting a controlled unbalance to the rotor and measuring its synchronous response. An active magnetic bearing can be employed as an exciter for turbomachine rotordynamics verifications (including a “non-synchronous testing”). Higher harmonics (particularly 2x) and an abnormal orbital motion are indicative of an excessive misalignment or a radial load. The fluid whirl vibrations because of bearing fluid interactions have frequencies slightly lower than 0.5x. The anisotropy can result in closely spaced, coupled “pairs” of natural frequencies (the “split resonances”). When using a high angular stiffness coupling, the driver and driven equipment will not behave as two independent turbomachines.