The majority of the experimental knowledge about QCD observables is contained in the excited hadron spectrum.The present thesis provides an ab-initio, non-perturbative determination of the excited meson and baryon spectrum, using the lattice regularization of QCD.We use a Hybrid Monte Carlo algorithm to generate seven ensembles with two flavors of dynamical Chirally Improved quarks. The advantages of the improved action lie in small discretization effects and frequent tunneling of topological sectors, reducing autocorrelation. The pion masses are in the range of 250 to 600 MeV, the results are extrapolated to the physical pion mass. Three further ensembles are generated to investigate finite volume effects and to perform the infinite volume limit for specific observables. The strange hadron spectrum is accessed using partial quenching for the strange quark. The variational method is applied to access excited states and also to investigate the content of the physical states.The latter applies in particular to the approximate C-parity of strange mesons, the singlet/octet mixing of Lambda baryons and the octet/decuplet mixing of Sigma and Xi baryons. The construction of interpolators is discussed for specific cases.In some baryon channels, Fierz identities force point-like interpolators to vanish exactly.We show that interpolators can be constructed nevertheless and propose two strategies, based on quark smearing and the Rarita-Schwinger condition, respectively. In general, our results compare nicely with experiment, and we even predict some new states and allow for insights concerning the content of the physical states.Part of the work has been published in journal articles, Phys. Rev. D 82 (2010) 034505 and Phys. Rev. D85 (2012) 034508, and further publications are in preparation.