Self-organized nanograting structures often generate inside the focal volume when an ultrashort pulse laser beam is focused in glass at a certain energy. One of the most promising applications of those nanogratings is fabrication of hollow glass microchannels through further chemical etching. For chemical etching of glass microchannels, usually the etching rate of laser modified regions is sensitive to the polarization of the laser beam since the orientation of the laser induced nanogratings is always perpendicular to the polarization direction of the laser beam. Ideally, a high etching rate occurs when the orientation of the nanograting is parallel to the laser translation direction. However, such polarization-dependent etching has some limitations to fabricate a 3D microchannel with complex geometries in glass since the translation direction of the laser beam frequently varies during laser irradiation and dynamical manipulation of polarization of the laser beam brings additional complexity of the experimental setup. In this contribution, we demonstrate our recent progress on polarization-insensitive etching in glass by using picosecond laser irradiation. An interesting phenomenon is that morphological transition from self-organized nanograting structures to randomly oriented nanocracks occurs in the laser modified regions in glass during the extension of the pulse duration of the laser beam from 270 fs to 10 ps. Moreover, the polarization dependence of the etching rate disappears when the pulse durations are stretched to above 4 ps, whereas an efficient etching rate can still be maintained due to the existence of randomly oriented nanocracks along the laser translation direction. Possible physical mechanism for the generation of the nanocracks and applications of polarization-insensitive selective etching in fused silica based on picosecond laser irradiation for fabrication of microfluidic devices and 3D glass printing are discussed.