X-ray imaging is a widely used imaging modality in the medical diagnostic field due to its availability, low cost, high spatial resolution, and fast image acquisition. X-ray photons in standard X-ray sources are polychromatic. Detectors that allow to extract the "color" information of the individual X-rays can lead to contrast enhancement, improved material identification or reduction of beam hardening artifacts at the system level, if we compare them with the widely spread energy integrating detectors. Today, in the field of computed tomography (CT), prototypes of clinical grade systems based on spectral photon counting detectors are currently available for clinical research from different companies. One of the key system components in that development is the X-ray photon detector. This article reviews the photon detection hardware, from the conversion of X-rays into electrical signals to the pulse processing electronics. A review of available photon counting application specific integrated circuits (ASICs) for spectroscopic X-ray imaging is presented with emphasis on the CT medical imaging application.