X-ray microscopes provide higher resolution than visible light microscopes. Wet, biological materials with a water thickness of up to about 10 microns can be imaged with good contrast using soft X-rays with wavelengths between the oxygen and carbon absorption edges (at 24 and 43 A). The Stony Brook group has developed and operates a scanning transmission X-ray microscope (STXM) at the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory. The microscope is used for imaging with a current resolution of 50 nm, and for elemental and chemical state mapping. Radiation damage imposes a significant limitation upon high resolution X-ray microscopy of room temperature wet specimens. Experience from electron microscopy suggests that cryo techniques allow vitrified specimens to be imaged repeatedly. This is due to the increased radiation stability of biological specimens in the frozen hydrated state. Better radiation stability has been shown recently with a cryo transmission X-ray microscope developed by the University of Göttingen, operating at the BESSY storage ring in Berlin, Germany. At Stony Brook, we are developing a cryo scanning transmission X-ray microscope (CryoSTXM) to carry out imaging and spectro-microscopy experiments on frozen hydrated specimens. This article will give an outlook onto the research projects that we plan to perform using the CryoSTXM.