Shape resonances are a ubiquitous phenomenon in electron–molecule scattering, in which the impinging electron is resonantly captured in a pseudo-bound state that is supported by the molecular potential. To study the electron scattering dynamics, we use time- and angle- resolved photoelectron spectroscopy here. With this technique, the transient evolution of the photoelectron angular distributions (PADs) from the ionization of an excited-state species can be measured. In the PADs, the electron–molecular-ion scattering dynamics are contained because the photoelectron necessarily interacts with the potential of the parent molecule as it escapes. The aim of this thesis is to investigate to what extent molecular dynamics, which are triggered by a pump laser pulse, are reflected in the PADs of the photoelectron spectra generated by an ionizing probe pulse, and how these effects can be rationalized in a photoelectron-scattering picture. Three experimental studies are covered in this thesis: In the first experiment, CF3I molecules are impulsively aligned in space by a short near-infrared pulse, which creates a rotational wave packet. During the revival of the rotational wave packet, PADs are measured for different molecular-axes distributions by photoionization with an ultrashort XUV pulse generated through high-order harmonic generation (HHG). Comparing the PADs thus obtained to the results of quantum-scattering calculations carried out with the ePolyScat suite of programs, we show that the alignment-dependent change in the PADs can be largely explained by two prominent shape resonances that contribute to the PADs in a distinctly different way geometrically. In the second experiment, we investigate the laser-assisted photoelectron recollisions that occur in strong-field ionization of atoms and molecules. We show how the differential scattering cross sections (DCSs) for the electron–molecular-ion collision process can be extracted from the resulting photoelectron spectrum. Then, we apply this approach to the investigation of the excited-state dynamics of I2 molecules that are prepared in the A or B state, leading to photodissociation and the creation of a vibrational wave packet, respectively. Again, by comparing to calculations carried out with ePolyScat, we conclude that the observed modulations in the DCSs of the rescattered electrons can be very well explained by considering two prominent shape resonances involved, the l=6 resonance of the diatomic molecular ion and the l=3 resonance of the free iodine atomic ion. In the third study, the time-resolved core-shell photoionization of dissociating halomethane molecules, namely CH3I and CH2ICl, is investigated employing ultrashort soft x-ray pulses provided by the free-electron laser FLASH in Hamburg, which are able to ionize the 4d shell of iodine close to the well-known “giant” photoionization resonance (again related to the l=3 shape resonance). We find that the dissociation clearly manifests as a shift of the 4d core-level binding energy, and that the time scale and temporal onset of this effect is distinctly different from that of the photoion measurements, which are commonly exploited to quantify the dissociation dynamics.