The work presents theoretical studies on nonlinear optical phenomena associated with light beams carrying orbital angular momentum, also called twisted light (TL). The thesis is divided into two main parts. The first part deals with the propagation of TL in a nonlinear medium with emphasis on self-focusing and defocusing of TL in a nonlinear dielectric medium. Utilizing the Wentzel-Kramers-Brillouin and the paraxial approximations, a differential equation for the beam width parameter is derived analytically. Next, the results are provided on the transmission and the reflection of TL through a dielectric multilayer structure containing phase-conjugating and calculated reflection and transmission coefficients are illustrated. The second part of the thesis focuses on the particle dynamics in TL, showing that the intensity distribution of TL results in trapping, guiding and acceleration of neutral helium atoms via the ponderomotive potential.