Recent theoretical work on the energy conversion by molecular motors coupled to nucleotide hydrolysis is reviewed. The most abundant nucleotide is provided by adenosine triphosphate (ATP) which is cleaved into adenosine diphosphate (ADP) and inorganic phosphate. The motors have several catalytic domains (or active sites), each of which can be empty or occupied by ATP or ADP. The chemical composition of all catalytic domains defines distinct nucleotide states of the motor which form a discrete state space. Each of these motor states is connected to several other states via chemical transitions. For stepping motors such as kinesin, which walk along cytoskeletal filaments, some motor states are also connected by mechanical transitions, during which the motor is displaced along the filament and able to perform mechanical work. The different motor states together with the possible chemical and mechanical transitions provide a network representation for the chemomechanical coupling of the motor molecule. The stochastic motor dynamics on these networks exhibits several distinct motor cycles, which represent the dominant pathways for different regimes of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses its direction of motion. In general, kinesin is found to be governed by the competition of three distinct chemomechanical cycles. The corresponding network representation provides a unified description for all motor properties that have been determined by single molecule experiments.