Glucagon-like peptide-1 receptor (GLP-1R) is a well-studied incretin hormone receptor and target of several therapeutic drugs for type 2 diabetes (T2D), obesity and, more recently, cardiovascular disease. Some signalling pathways downstream of GLP-1R may be responsible for drug adverse effects such as nausea, while others mediate therapeutic outcomes of incretin-based T2D therapeutics. Understanding the interplay between different factors that alter signalling, trafficking, and receptor activity, including biased agonism, single nucleotide polymorphisms and structural modifications is key to develop the next-generation of personalised GLP-1R agonists. However, these interactions remain poorly described, especially for novel therapeutics such as dual and tri-agonists that target more than one incretin receptor. Comparison of GLP-1R structures in complex with G proteins and different peptide and non-peptide agonists has revealed novel insights into important agonist-residue interactions and networks crucial for receptor activation, recruitment of G proteins and engagement of specific signalling pathways. Here, we review the latest knowledge on GLP-1R structure and activation, providing structural evidence for biased agonism and delineating important networks associated with this phenomenon. We survey current biased agonists and multi-agonists at different stages of development, highlighting possible challenges in their translational potential. Lastly, we discuss findings related to non-synonymous genomic variants of GLP1R and the functional importance of specific residues involved in GLP-1R function. We propose that studies of GLP-1R polymorphisms, and specifically their effect on receptor dynamics and pharmacology in response to biased agonists, could have a significant impact in delineating precision medicine approaches and development of novel therapeutics.