Since the isolation of graphene in 2004, two-dimensional crystals have attracted a lot of attention in a variety of scientific fields. Thus, Andre Geim and Kostya Novoselov were honoured with the Nobel Prize in 2010 for their findings. Ten years later, the interest in materials like graphene and single layer MoS2 is still growing. In order to actually implement these new materials in the plentitude of applications that are envisaged, new tools are needed. The purpose of this work is to investigate whether swift heavy ions (highly charged ions with typical energies ranging from 100 MeV to GeV) can be used as such a new tool for the modification of the morphology and doping of these materials. To obtain two-dimensional crystals of the highest quality, the mechanical exfoliation technique is used to prepare graphene and MoS2 single layers on various substrates. However, as the samples are prepared in ambient the resulting single layers are usually contaminated with adsorbates and water is intercalated between the crystal and the substrate. Furthermore, the presence of the substrate alone results in a significant change of the properties of two-dimensional crystals. Therefore graphene and MoS2 prepared on different substrates are investigated using non-contact atomic force microscopy and Kelvin probe force microscopy in situ to probe the contribution of adsorbates, intercalated water and the substrate itself under defined conditions. It has already been shown that graphene is folded upon swift heavy ion impact when irradiated under grazing incidence. In this work, the mechanism of the folding formation is studied and it will be shown that the size of the foldings can be controlled precisely by the energy of the ion, the incidence angle of the ion with respect to the sample surface and the choice of the substrate. In case of single layer MoS2 an additional modification to the morphology can be observed in form of nanoscale slit pores. The length of these slit pores can be controlled by the incidence angle again and the aspect ratio up to 1:600 (width:length). A mechanism for the formation of the slit pores is formulated: a thermal spike generated by the intense electronic excitation of the swift heavy ion is heating up the substrate on which MoS2 is attached. The temperature at the surface is exceeding the melting temperature of MoS2 and results in the formation of the slit pore. The last part of this thesis deals with the possibility of doping graphene using swift heavy ions. By preparing graphene samples without an intercalated water layer, the folding formation can be prevented. Instead, a surface track is created into the atomically thin carbon layer. This surface track significantly increases the hole charge carrier concentration in graphene and it will be shown that the surface tracks are created by implantation of Si atoms from the substrate due to the swift heavy ion irradiation.