From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made. From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equals) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.