Landscapes of investigation provide different learning environments from the paradigm of exercises. The move from exercises into landscapes of investigation is a move into new risk structures, but is also a move into new possibilities. When entering into landscapes of investigation, one cannot expect the communication to follow predictable patterns. Here, one enters an environment which calls for dialogue. I see dialogue as playing a fundamental role in establishing a critical activity, and as a consequence I consider working with landscapes of investigation to be an important feature of critical mathematics education. The exploration of landscapes is not restricted to particular groups of students. Any group of students can be invited into such landscapes: students at social risk, students in comfortable positions, students with disabilities, senior students, and university students in mathematics. Landscapes of investigation are constructions; they are contested, and they can come to include any kind of controversial issue.