The Hard X-ray FEL machine SwissFEL at the Paul Scherrer Institut in Switzerland is commissioned and transiting to user operation smoothly. FEL operation requires stringent requirements for the beam stability at the linac output, such as the electron bunch arrival time, peak current and beam energy. Among other things, a highly stable RF system is required to guarantee the beam stability. RF performance often dominates the overall performance and availability of FELs, and for this reason the SwissFEL RF system has been designed based on the state-of-the-art technologies that have enabled excellent RF stability, resulting in an arrival time jitter of ~10 fs rms and relative beam energy stability of 10^-4 rms. This paper aims to provide an understanding of the peak performance of the RF systems and to highlight possible limitations currently faced, focusing on the S-, C- and X-Band systems.