The laser beam quality is a topic of current interest. For a real laser, there exists hard-aperture optics more or less. On the other hand, the people are often concerned about the focusability of laser beams in the far field. The extension of the beam propagation factor (M~2 factor) to the apertured case is discussed. Three typical approaches to truncated beams, i.e. the generalized truncated second-moments method, asymptotic analysis and self-convergent-beam-width method, as well as their applications are analyzed. The power in the bucket (PIB) and β-parameter are used to characterize the beam quality in the far field. Then, some practical requirements for the laser beam quality and related characteristic parameters are studied. Finally, a brief discussion about the beam quality control of a complicated high-power laser system as a whole is made in this paper.