  By utilizing higher harmonics of undulator radiation, harmonic lasing is
helpful in the development of compact x-ray free electron lasers (FELs), i.e.
reducing its costs and sizes. Harmonic lasing of FELs have been experimentally
demonstrated in the low-gain FEL oscillators from terahertz, infrared to
ultraviolet spectral range. Based on the current status and future directions
of short-wavelength FELs in the worldwide, this paper reviews the progresses on
harmonic lasing of x-ray FELs, mainly concentrating on the recently proposed
harmonic lasing of x-ray FEL oscillators and further ideas on harmonic lasing
of single pass x-ray FEL amplifiers.
