In the photoemission process electrons are emitted from a solid upon excitation with UV light. From the measurement of their energy and momentum, angle-resolved photoemission spectroscopy (ARPES) allows to reconstruct the electronic properties of the solid. In addition, in spin-resolved ARPES the spin polarization P of the electrons is measured while maintaining energy and momentum resolution of ARPES, required to probe a dispersive state of a solid. The spin information is related to the spin polarization of the state under investigation, but can be modified during the photoemission process. Indeed, even when the electrons originate from a spin-degenerate initial state, they can acquire a finite P. This effect, ultimately due to a symmetry breaking in the experiment, occurs when different channels in the matrix elements describing the transition coherently interfere. In particular, P is related to the phase shift between the complex matrix elements associated to the interfering channels. This phase shift is also closely related to another quantity: the Eisenbud-Wigner-Smith (EWS) time delay. Despite the fundamental difficulties to properly define the concept of time in quantum mechanics, the EWS time delay, introduced to describe the electron scattering process, can be adapted to study the chronoscopy of photoemission. Nowadays, thanks to advances in laser technology, time-resolved spectroscopic techniques that reach attosecond resolution allow to measure relative EWS time delays between photoelectrons from different states. In this Thesis, an alternative indirect way to probe the photoemission process in the attosecond domain without time-resolved laser techniques will be presented. The link between P from dispersive states of a solid and the EWS time delay will be introduced. An analytical model will be discussed, where the dependence of P with binding energy is related to the EWS time delay of photoemission as a scattering process and the EWS time delay between the interfering channels. The first experimental determination of EWS time delays from dispersive states by SARPES will be also presented. Synchrotron radiation-based SARPES is the main technique used in this Thesis. Results for a single crystal of Cu(111) give EWS time delays of about 26 as for the free-electron-like sp bulk-derived band. The P of the d bands and of the 3p core levels of copper is also investigated. On the other hand, experiments on the strongly correlated cuprate superconductor BSCCO2212 show EWS time delays that are at least 3 times larger than in Cu(111). A double polarization feature is observed for the dispersive states, likely related to self-energy corrections in the photoemission process. Recent results on BSCCO2212 performed with laser-based SARPES will be also discussed. The results presented in this Thesis pave the way for a qualitatively new kind of information accessible by the SARPES technique, which is complementary to attosecond-resolved spectroscopies. The model presented sheds light on the spin polarization that is obtained by one-step model photoemission calculations, where the time information becomes also available. This approach could help to advance in the understandings of the physics of materials of interests, in particular electronic correlations, but also to better interpret the spin information experimentally obtained in SARPES, as well as to describe the basics of the quantum mechanics of the photoemission process itself.