Science is integral to society because it can inform individual, government, corporate, and civil society decision-making on issues such as public health, new technologies or climate change. Yet, public distrust and populist sentiment challenge the relationship between science and society. To help researchers analyse the science-society nexus across different geographical and cultural contexts, we undertook a cross-sectional population survey resulting in a dataset of 71,922 participants in 68 countries. The data were collected between November 2022 and August 2023 as part of the global Many Labs study "Trust in Science and Science-Related Populism" (TISP). The questionnaire contained comprehensive measures for individuals' trust in scientists, science-related populist attitudes, perceptions of the role of science in society, science media use and communication behaviour, attitudes to climate change and support for environmental policies, personality traits, political and religious views and demographic characteristics. Here, we describe the dataset, survey materials and psychometric properties of key variables. We encourage researchers to use this unique dataset for global comparative analyses on public perceptions of science and its role in society and policy-making.