A comprehensive experimental analysis of the dynamics of an ytterbium-doped fiber laser actively Q-switched (QS) using an intracavity acousto-optical modulator (AOM) is presented. It is shown that type of QS pulsing strongly depends on AOM repetition rate and pump power. In particular, at low repetition rates, including zero-rate, and at relatively high pump powers peculiar QS pulsing, switched by stimulated Brillouin scattering (SBS), is established in the laser. The cause of such kind of pulsing is the SBS-process boosted by spurious narrow-line CW lasing that arises in auxiliary low-Q cavity formed by an output coupler (in our experiments — fiber Bragg gratings) and weak reflections from blocked AOM. The parameters’ area where this regime occurs is limited by certain values of pump power and AOM repetition rate. At increasing AOM repetition rate or decreasing pump power spurious CW lasing is not attained in the system; consequently, the SBS type of QS fades, while “conventional” QS (CQS) lasing is established in the system and remains. However CQS pulsing strongly suffers the nonlinear-dynamics effects: depending on AOM repetition rate and pump power the laser switches to common P1, P2, or P3 attractors, when QS pulses arise at sub-harmonics of AOM repetition rate, or to the specific transient regimes between them, or to chaotic operation. These and other sides (e.g. pulse jittering) of operation of the QS ytterbium-doped fiber laser with AOM are under scope of the present review as they have big interest for practical applications.