X-ray phase contrast imaging (XPCI) using a single absorption grating and a hybrid semiconductor pixel detector is a newly introduced approach with great potential for application in medicine, biology and material research. In comparison with a conventional grating interferometer technique, which requires a multiple-exposure (phase-stepping) procedure, our method is greatly simplified, because both phase gradient and absorption images are obtained from just one exposure. Consequently, the approach can significantly reduce the time-consuming scanning and also possibly the unnecessary dose. Examples of application of the single-grating approach as an imaging tool for investigations in biology are presented. Particularly, we present the extension of our 1-D single grating method to a two-direction sensitive technique. The novel 2-D sensitive XPCI method is based on precise sub-pixel position determination of the X-ray pattern projected by the two-dimensional transmission grating directly from the pattern image. In a single exposure, phase gradient images in two perpendicular directions together with the conventional attenuation image are produced. Results of the proof-of-concept experiment are presented.