Quantum Chromodynamics (QCD) is well established as the gauge theory that describes the physics of strongly interacting matter. However, a derivation of the properties of baryonic and nuclear states directly from this fundamental theory is still one of the biggest challenges of theoretical physics. The Skyrme model is an effective field theory that aims to describe the phenomenolgy of low-energy QCD in a nonperturbative fashion, in which baryons and nuclei are understood as topological solitons, known as Skyrmions. In this talk, I will review recent developments on the application of the model to the description of the static properties and excitation spectrum of light nuclei, as well as the equation of state of cold, ultradense matter such as that at the core of neutron stars.