Insect pollinators of crops and wild plants are under threat globally and their decline or loss could have profound economic and environmental consequences. Here, we argue that multiple anthropogenic pressures - including land-use intensification, climate change, and the spread of alien species and diseases - are primarily responsible for insect-pollinator declines. We show that a complex interplay between pressures (eg lack of food sources, diseases, and pesticides) and biological processes (eg species dispersal and interactions) at a range of scales (from genes to ecosystems) underpins the general decline in insect-pollinator populations. Interdisciplinary research on the nature and impacts of these interactions will be needed if human food security and ecosystem function are to be preserved. We highlight key areas that require research focus and outline some practical steps to alleviate the pressures on pollinators and the pollination services they deliver to wild and crop plants.