In recent years, fractional calculus as a tool has been widely used in various fields of engineering. Compared with the constant order fractional calculus operator, the variable order fractional calculus operator can describe the physical properties of complex systems more accurately. As a powerful mathematical tool, the variable order fractional calculus modeling provides convenience for engineering modeling. On the basis of previous excellent research results, combined with the research results of domestic and foreign scholars in recent years, this paper makes a comprehensive review of the research of variable fractional calculus equations. The variable-order fractional differential equations(VO-FDEs), the variable-order time fractional convection-diffusion equations(VOTFC-DEs), the variable-order fractional reaction-diffusion equations(VOTFR-DEs), the variable-order fractional integral-differential equations(VO-FIDEs), the variable-order delay fractional differential equations(VO-DFDEs) and the variable-order fractional optimal control problems(V-FOCPs) are taken as the main research objects, which are introduced from several aspects of variable fractional calculus operator related definitions, models, numerical solutions and applications in engineering. It is found that most of the algorithms in recent years are based on polynomial algorithms, which can realize the transformation of variable order differential equations to algebraic equations by constructing different operation matrices. This review can provide reference for researchers in related fields.