Scientific objectivity and reliability are matters of fundamental importance both to science and in the public sphere, where they tend to be regarded with scepticism due to reporting of faulty or biased information, particularly in certain domains. In science studies, these qualities have been questioned in the light of two main characteristics of scientific activity: the inadequacy of data to determine theories, which opens the door to the possible influence of epistemic and value-based assumptions and prejudices, and the social character of scientific work, which may magnify their effect. Science education has a role to play in promoting informed trust in science and in improving science by preparing students to act positively either in the research field as future scientists or in the public domain as informed citizens. In this article, we systematize questions, responses, and arguments relating to the objectivity and trustworthiness of science that have been propounded in the philosophy, history, and sociology of science and which may contribute to an epistemologically sound conception of the subject in science education. We examine the kinds of bias that can affect science, the mechanisms available for dealing with them, and the arguments against treating them as a basis for blanket scepticism. The positions and arguments examined in this analysis generally imply that science is trustworthy and valuable, but confidence in science should be qualified, depending on the circumstances of each research program and the community that produces it, and they suggest means for improving the function and social role of science.