Organising teaching of a topic around a small number of "big ideas" has been argued by many to be important in teaching for deep understanding, with big ideas being able to link different activities and to be framed in ways that provide perceived relevance and routes into engagement. However it is our view that, at present, the significance of big ideas in classroom practice is underappreciated while their implementation in teaching is perceived as "unproblematic". In this paper we address these issues; while we draw on the experiences of two major research projects focusing on teachers' pedagogical reasoning, we attempt to investigate big ideas from a conceptual stance. While the domain is important, we argue that the source of big ideas should include reflection on issues of student learning and engagement as well as the domain. Moreover, big ideas should be framed in ways that are richer, more generative of teaching ideas and more pedagogically powerful than topic headings. This means framing them as a sentence, with a verb, that provides direction and ideas for teachers. We posit three different kinds of big ideas: big ideas about content, big ideas about learning and big ideas about the domain; the last two result in teachers having parallel agendas to their content agendas. In addition to discussing how pedagogically powerful big ideas can be constructed, we draw on data from highly skilled teachers to extend thinking about how teachers can use big ideas.