The perfection of methods and means of nondestructive testing and technical diagnostics is determined by the level of development of science and modern industrial technologies. The desire to develop technologies determines the extent and degree to which the monitoring of the state of substances, materials, products—and now the state of the natural environment—are becoming increasingly relevant. The methods and means of condition monitoring and the diagnostics of rolling bearings have been in development for more than 60 years. Despite some successes, however, there is currently no information concerning the veracity of means to completely resolve the bearing diagnostics problem. This paper provides a fairly brief overview of methods and means for monitoring the condition and diagnosis of rolling bearings and also describes one of the newest trends in this field—the analysis of the properties of the characteristic function of vibroacoustic (VA) signals in order to determine the condition of the objects of control and, in particular, rolling bearings. It is shown that the magnitude of the module and the area of the characteristic function of the VA signal are very effective criteria for assessing the technical condition of a rolling bearing.