X-ray imaging is a standard tool for the non-destructive inspection of the internal structure of samples. It finds application in a vast diversity of fields: medicine, biology, many engineering disciplines, palaeontology and earth sciences are just few examples. The fundamental principle underpinning the image formation have remained the same for over a century: the X-rays traversing the sample are subjected to different amount of absorption in different parts of the sample. By means of phase-sensitive techniques it is possible to generate contrast also in relation to the phase shifts imparted by the sample and to extend the capabilities of X-ray imaging to those details that lack enough absorption contrast to be visualised in conventional radiography. A general overview of X-ray phase contrast imaging techniques is presented in this review, along with more recent advances in this fast evolving field and some examples of applications.