Background: Programmes that provide scientists and engineers with support to engage in public policy have proliferated in the United States, with many opportunities available for training, networking and placements within government and government-facing organisations. This trend suggests that an evolution may be occurring at the science--policy interface. However, there is little extant data on the structure, aims and impacts of these programmes. Aims and objectives: This study maps the current landscape of US programmes seeking to train researchers at all career stages to engage in policy. We focus on Virginia, a state with a substantial number and diversity of programmes, to assess: (1) how they conceptualise their audiences, activities and impacts; and (2) which roles in policy and types of evidence use they address. Methods: We developed a database of US policy programmes (n=174) and conducted a case study of those in Virginia through surveys and interviews with their leaders (n=12). Findings: The majority (57%) of science policy programmes are state-based. These programmes include student organisations, government placements and fellowships, and academic certificates, degrees, and other trainings. While these reflect diverse models for how to engage researchers in policy, Virginia programme leaders across these categories similarly conceived long-term impacts, audiences and activities, researcher roles in policy, and types of decision-maker evidence use. And they perceived limited ability to implement evidence-based approaches within their programmes. Discussion and conclusion: Building additional programmatic capacity -- through shared learning and partnerships -- could lend support to this emerging trend in science policy with implications for US research and governance.