Understanding and engineering scanning tunneling microscopy (STM) image contrasts is of crucial importance in wide areas of surface science and related technologies, ranging from magnetic surfaces to molecular structures. Different STM tip effects on the image contrast are highlighted based on first principles calculations, going beyond the Tersoff-Hamann model, e.g., within 3D-WKB tunneling theory . Examples include highly oriented pyrolytic graphite , which is commonly used for STM calibration, and complex surface magnetic structures exhibiting non-collinear magnetic order, like recently popular topologically protected skyrmions . By comparing STM topographic data between experiment and large scale simulations, a statistical analysis of the tip apex structure is demonstrated for the first time . A combination of STM and X-ray photodiffraction helps the understanding of chirality transfer from molecules to crystal surfaces . Furthermore, two new developments of STM theories are presented: (i) an extension of Chen's derivative rule  for STM simulations including tip-orbital interference effects with demonstrated importance of such effects on the STM contrast for two surface structures: N-doped graphene and a magnetic Mn2H complex on the Ag(111) surface ; (ii) a combined tunneling charge and vector spin transport theory, which provides the first steps towards the theoretical modeling of high-resolution spin transfer torque imaging [3,7].
 K. Palotás et al., Front. Phys. 9, 711 (2014)
 G. Mándi et al., J. Phys.: Condens. Matter 26, 485007 (2014), Prog. Surf. Sci. 90, 223 (2015)
 K. Palotás et al., Phys. Rev. B 96, 024410 (2017), arXiv:1801.08375 (2018)
 W. Xiao et al., Nature Chem. 8, 326 (2016)
 C. J. Chen, Phys. Rev. B 42, 8841 (1990)
 G. Mándi, K. Palotás, Phys. Rev. B 91, 165406 (2015)
 K. Palotás et al., Phys. Rev. B 94, 064434 (2016)