G protein-coupled receptors (GPCRs) are integral membrane proteins with seven transmembrane domains. They are essential in intercellular communication in human physiology and represent important drug targets in human disease. While methodological advances, particularly in cryogenic electron microscopy (cryo-EM), have made more GPCRs amenable to structural studies, they remain challenging targets. During this project, the thyroid-stimulating hormone receptor (TSHR) and the β1-adrenoceptor (β1AR) were studied. The TSHR is a class A GPCR that belongs to the family of glycoprotein hormone receptors. It carries a large extracellular domain (ECD) that binds to the endogenous ligand, the thyroid stimulating hormone (TSH). In autoimmune diseases, antibodies bind to the ECD and can act as either agonists or antagonists. The aim was to investigate the structure of the previously uncharacterised full-length TSHR and gain insight into the activation mechanism. A lentivirus-based expression system for the TSHR in mammalian cells to produce sufficient quantities for structural studies by cryo-EM was developed. The purification conditions were optimised, so that the TSHR remained stable throughout the purification. Antibody fragments that activate the TSHR were purified. These components were used to assemble a stable active-state complex of antibody fragment, TSHR and heterotrimeric G protein. Vitrification of the complex was optimised, cryo-EM data were collected, and a low-resolution structure was determined. The β1AR is a class A GPCR, bearing little homology to the TSHR, which has been intensely studied and is structurally well characterised. The β1AR is of particular importance in the treatment of heart disease by beta blockers (receptor antagonists). However, current β1AR antagonists have off-target effects on the β2AR that worsens the symptoms of respiratory diseases. Novel, highly β1AR-selective antagonists have been developed, but the structural basis for their selectivity is unknown. Using these ligands, a humanised turkey β1AR was expressed and purified in complex with antibody fragments to increase the size of the complex and make it amenable to cryo-EM studies was. By using a new grid type, all-gold HexAuFoil grids, cryo-EM data of this complex could be collected and analysed.