High-$p_T$ parton propagation and quenching in the medium

Jet quenching stands out as one of the most striking phenomena measured in heavy-ion collisions. After being discovered at RHIC as a suppression of high-$p_T$ hadrons, with the development of reconstruction techniques capable of dealing with large backgrounds, it has also been confirmed in a wide range of measurements involving fully reconstructed jets. The observed suppression patterns are generally understood as arising from interactions with a color deconfined medium, corroborating the role of jets as probes of the hot and dense matter created in ultrarelativistic heavy-ion collisions. In this proceeding, we report on recent theoretical developments related to how jet fragmentation inside the medium is affected by energy-loss processes. In particular, it is shown how a novel Sudakov suppression factor affects the single-inclusive jet spectrum at high-$p_T$. These developments provide first steps toward a unified theoretical understanding of the quenching of hadrons and jets, accompanied by substructure modifications.