Living cells represent open, nonequilibrium, self-organizing, and dissipative systems maintained with the continuous supply of outside and inside material, energy, and information flows. The energy in the form of adenosine triphosphate is utilized in biochemical cycles, transport processes, protein synthesis, reproduction, and performing other biological work. The processes in molecular and cellular biological systems are stochastic in nature with varying spatial and time scales, and bounded with conservation laws, kinetic laws, and thermodynamic constraints, which should be taken into account by any approach for modeling biological systems. In component biology, this review focuses on the modeling of enzyme kinetics and fluctuation of single biomolecules acting as molecular motors, while in systems biology it focuses on modeling biochemical cycles and networks in which all the components of a biological system interact functionally over time and space. Biochemical cycles emerge from collective and functional efforts to devise a cyclic flow of optimal energy degradation rate, which can only be described by nonequilibrium thermodynamics. Therefore, this review emphasizes the role of nonequilibrium thermodynamics through the formulations of thermodynamically coupled biochemical cycles, entropy production, fluctuation theorems, bioenergetics, and reaction-diffusion systems. Fluctuation theorems relate the forward and backward dynamical randomness of the trajectories or paths, bridge the microscopic and macroscopic domains, and link the time-reversible and irreversible descriptions of biological systems. However, many of these approaches are in their early stages of their development and no single computational or experimental technique is able to span all the relevant and necessary spatial and temporal scales. Wide range of experimental and novel computational techniques with high accuracy, precision, coverage, and efficiency are necessary for understanding biochemical cycles.