We articulate a student perspective on task design in mathematics education, foregrounding a dynamic relationship between intentions of task designers, teachers, and students. First, we characterize a student perspective on task design. Second, we provide theoretical perspectives that we use as tools to account for different facets of task design from a student perspective. Third, we elaborate on "tensions of intentions" between designers, teachers, and students when considering the use of tasks to promote students' mathematical learning. Fourth, we address mathematical tasks and the student: characterizing task context from a student perspective, contrasting reflective and emergent task design, and discussing theoretical and methodological approaches that take into account the student perspective. We conclude with implications for research and practice.