Non-invasive techniques utilizing X-ray radiation offer a significant advantage in scientific investigations of painted arts and other cultural artefacts such as painted artworks or statues. In addition, there is also great demand for a mobile analytical and real-time imaging device given the fact that many fine arts cannot be transported. The highly sensitive hybrid semiconductor pixel detector, Timepix, is capable of detecting and resolving subtle and low-contrast differences in the inner composition of a wide variety of objects. Moreover, it is able to map the surface distribution of the contained elements. Several transmission and emission techniques are presented which have been proposed and tested for the analysis of painted artworks. This study focuses on the novel techniques of X-ray transmission radiography (conventional and energy sensitive) and X-ray induced fluorescence imaging (XRF) which can be realised at the table-top scale with the state-of-the-art pixel detector Timepix. Transmission radiography analyses the changes in the X-ray beam intensity caused by specific attenuation of different components in the sample. The conventional approach uses all energies from the source spectrum for the creation of the image while the energy sensitive alternative creates images in given energy intervals which enable identification and separation of materials. The XRF setup is based on the detection of characteristic radiation induced by X-ray photons through a pinhole geometry collimator. The XRF method is extremely sensitive to the material composition but it creates only surface maps of the elemental distribution. For the purpose of the analysis several sets of painted layers have been prepared in a restoration laboratory. The composition of these layers corresponds to those of real historical paintings from the 19th century. An overview of the current status of our methods will be given with respect to the instrumentation and the application in the field of cultural heritage.