The quantum mechanical description of fundamental processes in an intense laser field consists of the calculation of corresponding transition matrix elements, which involve the exact wave function of an electron dynamically interacting with an intense laser field. This wave function obeys the time-dependent Schrodinger equation (TDSE), whose solution for a given atomic potential and electron-laser interaction cannot be found in a closed analytic form. This obstacle can be overcome either by getting this wave function numerically from the TDSE or by applying some approximations ensuring different levels of accuracy for the transition matrix element. In this talk I will give a short overview of the recently developed adiabatic approach, which is applied for description of the joint interaction of an intense IR and attosecond XUV pulses with unpolarized atom. I also will discuss how to utilize adiabatic approach for the description of nonlinear phenomena in atoms jointly interacting with an intense IR and attosecond XUV pulses by developing specific perturbation theory for IR-dressed atoms. The physics of new nonlinear XUV-induced phenomena as XUV-assisted high harmonic generation, XUV rectification effect, second harmonic generationg of the XUV field will be discussed with further application to the attosecond and IR pulse metrology.