Semiclassical models based on classical trajectories for the description of the electron motion in the continuum are a powerful tool of strong-field, ultrafast, and attosecond physics. The semiclassical models allow us to identify the specific mechanism of a phenomenon of interest and visualize it in terms of classical trajectories. Often these models are also computationally simple. In the present work we developed a range of new semiclassical models and applied them to various strong-field phenomena. Among these are: capture of electrons into Rydberg states, sequential multiple ionization, above-threshold ionization of the hydrogen molecule, multielectron effects due to the laser-induced polarization of the atomic ion, and strong-field holography with photoelectrons. We also used the semiclassical simulations to understand the results obtained using quantum optimal control theory, namely, optimization of the high-harmonic yield by shaping of the driving pulse. We developed a method capable of retrieving effective single-active electron potentials, which are required for semiclassical simulations. In this method the single-active electron potential is found as the result of an optimization procedure aimed at reproducing given photoelectron momentum distributions. Finally, we applied deep learning to retrieve the internuclear distance in a molecule ionized by a strong laser pulse from the photoelectron momentum distribution. The results of this thesis will serve as a basis for development of new generation of semiclassical models that are expected to combine accurate description of the ionization step, the ability to account for interference and multielectron effects, and numerical efficiency. The emergence of such models will open new perspectives in the theory of laser-matter interaction.