The production of a Higgs boson in association with top quark pairs (ttH) or single top quarks (tH) is the direct way to observe the top-Yukawa coupling at the LHC. In contrast to the production of a Higgs boson via gluon-gluon-fusion or the decay of the Higgs boson into two photons, where the top quark contributes significantly to both processes through loop diagrams, no assumptions on other particles or BSM physics have to be made. This presentation reviews the latest results on searches for ttH and tH production by the ATLAS and CMS collaborations. In order to observe these rare Higgs boson production modes, heavy usage of multivariate analysis techniques is necessary to increase the sensitivity.