Laser plasma sources of soft x-rays and extreme ultraviolet (EUV) developed in our laboratory for application in various areas of technology and science are presented. The sources are based on a laser-irradiated gas puff target approach. The targets formed by pulsed injection of gas under high-pressure are irradiated with nanosecond laser pulses from Nd:YAG lasers. We use commercial lasers generating pulses with time duration from 1ns to 10ns and energies from 0.5J to 10J at 10Hz repetition rate. The gas puff targets are produced using a double valve system equipped with a special nozzle to form a double-stream gas puff target which secures high conversion efficiency without degradation of the nozzle. The use of a gas puff target instead of a solid target makes generation of laser plasmas emitting soft x-rays and EUV possible without target debris production. The sources are equipped with various optical systems, including grazing incidence axisymmetric ellipsoidal mirrors, a “lobster eye” type grazing incidence multi-foil mirror, and an ellipsoidal mirror with Mo/Si multilayer coating, to collect soft x-ray and EUV radiation and form the radiation beams. In this paper new applications of these sources in various fields, including soft x-ray and EUV imaging in nanoscale, EUV radiography and tomography, EUV materials processing and modification of polymer surfaces, EUV photoionization of gases, radiobiology and soft x-ray contact microscopy are reviewed.