In this thesis we describe the extension and implementation of the Sternheimer- GW method to a first-principles pseudopotential framework based on a planewaves basis. The Sternheimer-GW method consists of calculating the GW self-energy operator without resorting to the standard expansion over unoccupied Kohn- Sham electronic states. The Green's function is calculated by solving linear systems for frequencies along the real axis. The screened Coulomb interaction is calculated for frequencies along the imaginary axis using the Sternheimer equa- tion, and analytically continued to the real axis. We exploit novel techniques for generating the frequency dependence of these operators, and discuss the imple- mentation and efficiency of the methodology. We benchmark our implementation by performing quasiparticle calculations on common insulators and semiconductors, including Si, diamond, LiCl, and SiC. Our calculated quasiparticle energies are in good agreement with the results of fully-converged calculations based on the standard sum-over-states approach and experimental data. We exploit the methodology to calculate the spectral func- tions for silicon and diamond and discuss quasiparticle lifetimes and plasmaronic features in these materials. We also exploit the methodology to perform quasiparticle calculations on the 2-dimensional transition metal dichalcogenide system molybdenum disulfide (MoS₂). We compare the quasiparticle properties for bulk and monolayer MoS2 , and identify significant corrections at the GW level to the LDA bandstructure of these materials. We also discuss changes in the frequency dependence of the electronic screening in the bulk and monolayer systems and relate these changes to the quasiparticle lifetimes and spectral functions in the two limits.