Vibrationally resolved electronic spectra of polyatomic molecules provide valuable information about the quantum properties of both electrons and nuclei. This chapter reviews the recent progress in ab initio semiclassical calculations of such spectra, based on the thawed Gaussian approximation and its extensions. After reviewing molecular quantum dynamics induced by the interaction with electromagnetic field and the most common semiclassical approximations to quantum dynamics, we explain details of the thawed Gaussian approximation and its variants. Next, we discuss the time-dependent approach to steady-state and time-resolved electronic spectroscopy, and review several standard models that facilitate interpreting vibrationally resolved electronic spectra. Finally, we present the on-the-fly ab initio implementation of the thawed Gaussian approximation and provide several examples of both linear and pump-probe spectra computed with this methodology, which, at a low additional cost and without sacrificing the ease of interpretation, outperforms the standard global harmonic approaches.