As humans age, the functional organisation of their brain networks undergoes complex changes that are associated with observed changes in cognition. Both genetics and the environment play a crucial role in influencing changes in the network topology of the ageing brain. In addition, the network topology is influenced by age-related brain diseases. To date, there is a paucity of population-based studies investigating the contributions of age, genetic and environmental factors, and brain disease to the architecture of the functional brain networks. The broad aim of this thesis, therefore, was to examine the influence of genetics, environmental factors, and disease-states on functional brain networks in older individuals using the United Kingdom (UK) Biobank data (N~18,455; ages 44-80 years). To study functional brain networks, I modelled large-scale brain networks from resting-state functional magnetic resonance imaging (fMRI) scans using graph theory, defined by a collection of nodes (brain regions) and edges (magnitude of temporal correlation in activity on fMRI between two brain regions). Four studies are reported in the thesis. In the first study, I investigated the genetic determinants of functional brain networks. I first estimated single nucleotide polymorphism (SNP) heritability (h2). Subsequently, genome-wide association studies (GWAS) were performed to identify genetic variants associated with each graph theory measure. Gene-based association analysis was carried out to uncover gene-level associations, and the functional consequences of the significant genetic variants were explored. As brain reorganisation of the functional networks has been differentially observed with ageing in the two sexes, I examined in the second study how age and sex are associated with the topology of functional brain networks in association with cognitive performance. In the third study, I examined the association of sleep and other lifestyle factors such as exercise, alcohol, and smoking, with functional network properties. In the final study, I studied how disease phenotypes, in particular depressive symptoms, influence functional network properties. This thesis provides several novel contributions to the literature by identifying important genetic, environmental, and disease-related factors that are associated with measures of functional networks in the ageing brain. The findings highlight biological pathways relevant to the ageing human brain functional network integrity and diseases that affect it.