Strong laser fields are a valuable tool to study the electron dynamics in atoms and molecules. A prominent strong-field process is the above-threshold ionization (ATI). Recent advances in the generation of intense laser beams at mid-infrared wavelengths enable the investigation of ATI in a new parameter range. Moreover, laser beams with a sophisticated spatial structure as a result of an orbital angular momentum (twisted light) have found applications in the strong-field regime. In this dissertation, we theoretically investigate ATI driven by mid-infrared and twisted light beams. We show that their spatial dependence has a pronounced impact on the ionization dynamics due to nondipole interactions. Therefore, we develop a general theoretical approach to ATI that incorporates this spatial structure: in order to extend the strong-field approximation (SFA), we construct nondipole Volkov states which describe the photoelectron continuum dressed by the laser field. The resulting nondipole SFA allows the treatment of ATI driven by spatially structured laser fields. We apply this SFA to the ATI driven by plane-wave laser beams and show that peak shifts in the photoelectron momentum distributions can be computed in good agreement with experiments. As a second application, we consider the ATI driven by standing waves, known as high-intensity Kapitza-Dirac effect. Here, we calculate the momentum transfer to photoelectrons for elliptically polarized standing waves and demonstrate that low- and high-energy photoelectrons exhibit different angular distributions. Finally, we investigate the ATI of localized atomic targets driven by few-cycle Bessel pulses. We demonstrate that the photoelectrons can be emitted along the propagation direction of the pulse owing to longitudinal electric field components. Moreover, the ATI spectra depend on both the opening angle and the orbital angular momentum of the Bessel pulse. We also discuss the extension of this work towards long pulses.