We present our recent results, related to nanoscale imaging in the extreme ultraviolet (EUV) and soft X-ray (SXR) spectral ranges and demonstrate three novel imaging systems recently developed for the purpose of obtaining high spatial resolution images of nanoscale objects with the EUV and SXR radiations. All the systems are based on laser-plasma EUV and SXR sources, employing a double stream gas puff target. The EUV and SXR full field microscopes-operating at 13.8 nm and 2.88 nm wavelengths, respectively-are currently capable of imaging nanostructures with a sub-50 nm spatial resolution with relatively short (seconds) exposure times. The third system is a SXR contact microscope, operating in the "water-window" spectral range (2.3-4.4 nm wavelength), to produce an imprint of the internal structure of the investigated object in a thin surface layer of SXR light sensitive poly(methyl methacrylate) photoresist. The development of such compact imaging systems is essential to the new research related to biological science, material science, and nanotechnology applications in the near future. Applications of all the microscopes for studies of biological samples including carcinoma cells, diatoms, and neurons are presented. Details about the sources, the microscopes, as well as the imaging results for various objects will be shown and discussed.