In the global quest to renounce from fossil fuels, a large demand for the renewable production of hydrogen via water electrolysis exists. In this context, the solid oxide electrolyzer (SOE) is an interesting technology due to its high efficiency resulting from elevated operating temperatures of up to 900 °C. Physical modeling plays a vital role in the development of SOEs, as it lowers experimental costs and provides insight where measurements reach limits. A main challenge for modeling SOEs is the multitude of physical effects, occurring and interacting on various spatial and temporal scales. This requires assumptions and simplifications, particularly when increasing scope and dimensions of a model. In this review, we discuss the different approaches currently available in literature.