This review covers all three unsteady-state fixed-bed processes important in chemical engineering, namely, heat transfer from a hot gas to a cold fixed bed (heat regenerator), ad-and desorption of a gas for a Langmuir and a linear isotherm, and regeneration of a coked catalyst by coke burn-off as an important example of a transient gas-solid process. Albeit of inherent differences, the processes have strong analogies. For example, a moving heat or mass transfer zone, spreading or with constant pattern behavior, is formed. For each case, numerical and suitable analytical solutions for process design either selected from literature or developed in this work are derived and compared. Experimental data, if available, are also considered.