We present the first lasing results of SwissFEL, a hard X-ray free-electron laser (FEL) that recently came into operation at the Paul Scherrer Institute in Switzerland. SwissFEL is a very stable, compact and cost-effective X-ray FEL facility driven by a low-energy and ultra-low-emittance electron beam travelling through short-period undulators. It delivers stable hard X-ray FEL radiation at 1-A wavelength with pulse energies of more than 500 mu J, pulse durations of similar to 30 fs (root mean square) and spectral bandwidth below the per-mil level. Using special configurations, we have produced pulses shorter than 1 fs and, in a different set-up, broadband radiation with an unprecedented bandwidth of similar to 2%. The extremely small emittance demonstrated at SwissFEL paves the way for even more compact and affordable hard X-ray FELs, potentially boosting the number of facilities worldwide and thereby expanding the population of the scientific community that has access to X-ray FEL radiation.