A couple of decades ago, x-ray tomography was a technique largely reserved for a few specialists fromthe hospitals' diagnostic departments and university based reseach groups. But during the last 20 yearsx-ray imaging has become much more available outside these narrow circles as a method to help theadvancement of many dierent academic and industrial elds.In this thesis I describe my work on developing the techniques within the eld and studying their possibleapplications as well as my collaboration with external researchers, applying x-ray imaging methodsto answer scientic questions within their particular elds.For the sake of completeness I start my thesis from the electric eld equation. From there I derivethe transport of intensity equation, the Fresnel propagator function and the basic formula of propagatedintensity used in holotomography. I also sketch the principles behind the magnication eect andinteractions between x-rays and matter.From these fundamental formulas and principles, I move on to describe the practical aspects of xrayimaging in more detail. I describe the basis of the dierent contrast mechanisms in absorption,holotomography and grating interferometry. I have also included a description of the basic principlesbehind tomogram reconstruction.Next, I describe my work relating to image construction from grating interferometer data, boththe adaptive-period sine tting method and the anisotropic tomogram reconstruction algorithm I havedeveloped.Thereafter I move on to describe my work investigating the applicability of the grating interferometerdark-eld signal for detecting sub-resolution sized cracks in a solid material and for detecting misalignedbers in a ber composite material.In the next chapter I introduce the ideas and main conclusions from my collaboration with researchersfrom other academic elds. Finally, I sum up my work and give my view on the future possibilities andchallenges within the eld.