This paper was written in honor of Prof. Viktor Olimpanovich Kononenko from Ukraine and takes into account reports of recent progress about non-ideal vibrating systems (NIS) published in the period from 2004 to 2017. New and old studies of NIS, with limited power supply (small DC motors or electrodynamical shakers), are usually used in laboratory tests, and therefore, the investigation of mutual interactions of driven and driving sub-system is very important. In this paper, main properties of NIS have been reviewed, such as the Sommerfeld effect, i.e., jump phenomena and the increase in power supply that is required by an excitation source operating near resonance; the possibility of saturation phenomenon occurrence, i.e., the transference of energy from higher frequency and lower amplitude to lower frequency and higher amplitude mode; and the existence of regular (periodic motion) and irregular (chaotic motion) behaviors, depending on the value of control parameters (voltage of a DC motor). This paper is divided into two goals: on the one hand will be treated about NIS and on the other hand will be provided an overview of the main engineering applications, analyzing their physical phenomena involved and the adequate methodologies to deal with them.