In this thesis, I used atomistic and micromagnetic model to study the dynamics behaviour of the domain wall and skyrmion in confined nanostructures driven by applied magnetic field, spin polarized current and voltage control magnetic anisotropy gradient. I also studied the thermal behaviour of the magnetic skyrmion in magnetic ultra-thin film. I study the domain structure and the magnetic switching in the Permalloy (Fe20Ni80) nanoscale magnetic junctions with different thicknesses by using micromagnetic simulations. My work shows that the nanoscale magnetic junction has the potential to be used as a building block for future spin-based data storage or logic computing technologies. The current-driven skyrmion motion in a narrow ferromagnetic nano-track with voltage-controlled magnetic anisotropy (VCMA) is studied numerically. The skyrmionium dynamics in a nano-track with voltage-controlled perpendicular magnetic anisotropy (VCMA) also has been reported. The results provide guidelines for practical realization of the skyrmion-based information channel, diode, and skyrmion-based electronic devices such as racetrack memory. The thermal-induced phase transition to a skyrmion state in IrCoPt has been demonstrated by the atomistic simulations parametrised from ab-initio calculations which include long-range exchange interactions. The simulation results give a clear vision of the thermal-induced behaviour in a chiral magnetic thin film.