It is generally accepted that dynamic voltage scaling (DVS) is one of the most effective techniques of energy minimization for real-time applications in embedded system design. The effectiveness comes from the fact that the amount of energy consumption is quadractically proportional to the voltage applied to the processor. The penalty is the execution delay, which is linearly and inversely proportional to the voltage. According to the granularity of tasks to which voltage scaling is applied, the DVS problem is divided into two subproblems: inter-task DVS problem, in which the determination of the voltage is carried out on a task-by-task basis and the voltage assigned to the task is unchanged during the whole execution of the task, and intra-task DVS problem, in which the operating voltage of a task is dynamically adjusted according to the execution behavior to reflect the changes of the required number of cycles to finish the task before the deadline. Frequent voltage transitions may cause an adverse effect on energy minimization due to the increase of the overhead of transition time and energy. In addition, DVS needs to be carefully applied so that the dynamically varying chip temperature should not exceed a certain threshold because a drastic increase of chip temperature is highly likely to cause system function failure. This paper reviews representative works on the theoretical solutions to DVS problems regarding inter-task DVS, intra-task DVS, voltage transition, and thermal-aware DVS.