In this meta-analysis, we synthesize the results of 24 studies using the Colorado Learning Attitudes about Science Survey (CLASS) and the Maryland Physics Expectations Survey (MPEX) to answer several questions: (1) How does physics instruction impact students' beliefs? (2) When do physics majors develop expert-like beliefs? and (3) How do students' beliefs impact their learning of physics? We report that in typical physics classes, students' beliefs deteriorate or at best stay the same. There are a few types of interventions, including an explicit focus on model-building and (or) developing expertlike beliefs that lead to significant improvements in beliefs. Further, small courses and those for elementary education and nonscience majors also result in improved beliefs. However, because the available data oversamples certain types of classes, it is unclear whether these improvements are actually due to the interventions, or due to the small class size, or student populations typical of the kinds of classes in which these interventions are most often used. Physics majors tend to enter their undergraduate education with more expertlike beliefs than nonmajors and these beliefs remain relatively stable throughout their undergraduate careers. Thus, typical physics courses appear to be selecting students who already have strong beliefs, rather than supporting students in developing strong beliefs. There is a small correlation between students' incoming beliefs about physics and their gains on conceptual mechanics surveys. This suggests that students with more expertlike incoming beliefs may learn more in their physics courses, but this finding should be further explored and replicated. Some unanswered questions remain. To answer these questions, we advocate several specific types of future studies: measuring students' beliefs in courses with a wider range of class sizes, student populations, and teaching methods, especially large classes with very innovative pedagogy and small classes with more typical pedagogy; analysis of the relationship between students' beliefs and conceptual understanding including a wide variety of variables that might influence each; and analysis of large data sets from a variety of classes that track individual students rather than averaging over classes.