The existence of multi-axial states of stress cannot be avoided in elevated temperature components. It is essential to understand the associated failure mechanisms and to predict the lifetime in practice. Although metal creep has been studied for about 100 years, many problems are still unsolved, in particular for those involving multi-axial stresses. In this work, a state-of-the-art review of creep analysis and engineering design is carried out, with particular emphasis on the effect of multi-axial stresses. The existing theories and creep design approaches are grouped into three categories, i.e., the classical plastic theory (CPT) based approach, the cavity growth mechanism (CGM) based approach and the continuumdamage mechanics (CDM) based approach. Following above arrangements, the constitutive equations and design criteria are addressed. In the end, challenges on the precise description of the multi-axial creep behavior and then improving the strength criteria in engineering design are presented.