Writing is a critical skill for modern science, enabling collaboration, scientific discourse, public outreach, and more. Accordingly, it is important to consider how physicists and astronomers are trained to write. This study aims to understand the landscape of science writing education, specifically in physics and astronomy, in higher education in the United States. An online survey probing various aspects of their writing training in both undergraduate and graduate school was administered to 515 participants who have obtained training in physics and/or astronomy, or related fields, at the level equal to or beyond upper-division undergraduate study. Humanities and writing requirement courses appear to have a key role in general writing education, while laboratory courses and feedback from mentors are the dominant modes of science writing education in undergraduate and graduate school, respectively. There is substantial variation in the quality of writing education in physics and astronomy, often dependent on the student's institution and/or mentor. Some participants also report that their success in disciplinary writing was a result of a solid foundation from K-12 education and/or self-direction toward resources; such reliance on past experiences and student background may contribute to inequality in the field. Many participants also stated a clear desire for more structured writing training to be available in the field. We provide suggestions for how to implement such training to meet the needs of the community identified in the survey.