Dynamical processes in chemistry are governed by the quantum mechanical nature of molecules exhibiting quantum effects like tunnelling and interference. An accurate description of these effects in complex chemical systems has proven to be a tremendous challenge over many decades. One promising avenue to study quantum dynamical effects in chemical systems is the semiclassical (SC) framework, so called because it captures quantum effects by exploiting ensembles of classical trajectories. The work presented in this thesis aims to highlight the many wonderful features of the SC framework \textemdash ~its versatile ability to describe varied problems at the frontier of physical chemistry and chemical physics, its diversity in variants that range in accuracy and numerical cost for simulating quantum effects in these problems, and perhaps most importantly, the insights it provides into the deep connections between quantum and classical dynamics.