The increasing availability of quantum-chemical data on surface reaction intermediates invites to revisit unresolved mechanistic issues in heterogeneous catalysis. One such an issue of particular current interest is the molecular basis of the Fischer-Tropsch reaction. Here we review current molecular understanding of this reaction that converts synthesis gas into longer hydrocarbons where we especially elucidate recent progress due to the contributions of computational catalysis. This perspective highlights the theoretical approach to heterogeneous catalysis that aims for kinetic prediction from quantum-chemical first principle data. Discussion of the Fischer-Tropsch reaction from this point of view is interesting because of the several mechanistic options available for this reaction. There are many proposals on the nature on the monomeric single C atom containing intermediate that is inserted into the growing hydrocarbon chain as well as on the nature of the growing hydrocarbon chains themselves. Two dominant conflicting mechanistic proposals of the Fischer-Tropsch reaction that will be especially compared are cleavage of the C-O bond of CO before incorporation of a CHx species into the growing hydrocarbon chain (the carbide mechanism) or after incorporation into the growing hydrocarbon chain (the CO insertion mechanism). The choice of a particular mechanism has important kinetic consequences. Since it is based on molecular information it also affects the structure sensitivity of this particular reaction and hence influences choice of catalyst composition. We will show how quantum-chemical information on the relative stability of relevant reaction intermediates and estimates of the rate constants of corresponding elementary surface reactions provides a firm foundation to the kinetic analysis of such reactions and allows to discriminate between the different mechanistic options. The paper will be concluded with a short perspective section dealing with needs for future research. Many of the current key questions on the physical chemistry as well as computational study of heterogeneous catalysis relate to particular topics for further research on fundamental aspects of Fischer-Tropsch catalysis.