The paper gives a review of investigations on generation of soft X-rays and EUV using a gas puff target irradiated with high-power laser pulses performed during last few years. In the studies a newly developed double-stream gas puff target approach was used. The gas puff targets were irradiated with various lasers, including Nd:glass, Kr:F, Nd:YAG, and iodine lasers. The aim of the studies was to develop efficient and debris-free laser plasma X-ray and EUV sources for applications in microscopy, lithography, micro-and nanotechnology.