All-inorganic perovskite nanocrystals (NCs) with enhanced environmental stability are of particular interest for optoelectronic applications. Here we report on the formulation of CsPbX3 (X is Br or I) inks for inkjet deposition and utilise these NCs as photosensitive layers in graphene photodetectors, including those based on single layer graphene (SLG) as well as inkjet-printed graphene (iGr) devices. The performance of these photodetectors strongly depends on the device structure, geometry and the fabrication process. We achieve a high photoresponsivity, R > 106 A W-1 in the visible wavelength range and a spectral response controlled by the halide content of the perovskite NC ink. By utilising perovskite NCs, iGr and gold nanoparticle inks, we demonstrate a fully inkjet-printed photodetector with R ≈ 20 A W-1, which is the highest value reported to date for this type of device. The performance of the perovskite/graphene photodetectors is explained by transfer of photo-generated charge carriers from the perovskite NCs into graphene and charge transport through the iGr network. The perovskite ink developed here enabled realisation of stable and sensitive graphene-based photon detectors. Compatibility of inkjet deposition with conventional Si-technologies and with flexible substrates combined with high degree of design freedom provided by inkjet deposition offers opportunities for partially and fully printed optoelectronic devices for applications ranging from electronics to environmental sciences.