In this thesis, density functional theory is employed in the study of two kinds of systems that can be considered to be biomimetic in their own ways. First, three binuclear metal complexes, synthesized by the group of Prof. Ebbe Nordlander, have been investigated. The complexes are designed to resemble the active sites of phosphatase enzymes and have been examined in complexes where either two Zn(II) ions or one Fe(III) and one Mn(II) ion are bound. These dinuclear compounds were studied as catalysts for the hydrolysis of bis(2,4-dinitrophenyl) phosphate and the transesterification of 2-hydroxypropyl p-nitrophenyl phosphate, which are model systems for the same reactions occurring in DNA or RNA. It was found that the two reactions take place in similar ways: a hydroxide ion that is terminally bound to one of the metal centers acts either as a nucleophile in the hydrolysis reaction or as a base in the transesterification. The leaving groups depart in an effectively concerted manner, and the formed catalyst-product complexes are predicted to be the resting states of the catalytic cycles. The rate-determining free energy barriers are identified from the catalyst-product complex in one catalytic cycle to the transition state of nucleophilic attack in the next. Another type of biomimetic modeling is made with an aim of imitating the conceptual features of selective binding of guests and screening them from solute-solvent interactions. Such features are found in so-called nanocontainers, and this thesis is concerned with studies of two capsules synthesized by the group of Prof. Julius Rebek, Jr. First, the cycloaddition of phenyl acetylene and phenyl azide has experimentally been observed to be accelerated in the presence of a capsule. Computational studies were herein performed on this system, and a previously unrecognized structure of the capsule is discovered. Two main factors are then identified as sources of the rate acceleration compared to the uncatalyzed reaction, namely the reduction of the entropic component and the selective destabilization of the reactant supercomplex over the transition state. In the second capsule study, the alkane binding trends of a water-soluble cavitand was studied. It is found that implicit solvation models fail severely in reproducing the experimental equilibrium observed between binding of n-decane by the cavitand monomer and encapsulation in the capsule dimer. A mixed explicit/implicit solvation protocol is developed to better quantify the effect of hydrating the cavitand, and a simple correction to the hydration free energy of a single water molecule is proposed to remedy this. The resulting scheme is used to predict new hydration free energies of the cavitand complexes, resulting in significant improvement vis-à-vis experiments. The computational results presented in this thesis show the usefulness of the quantum chemical calculations to develop understanding of experimental trends observed for substrate binding and catalysis. In particular, the methodology is shown to be versatile enough such that experimental observations can be reproduced for such diverse systems as studied herein. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 5: Manuscript.</p>