Digital assessment of mathematics is becoming widespread, but still comes with limitations and constraints. A central question is how to design digital tests that assess mathematical knowledge in a valid way. Based on literature on validity and on assessment with and through technology, we identify arguments for and opportunities of digital assessment of mathematics, as well as its main issues. Through three case descriptions, different ways to design digital tests are explored. As a conclusion, we make a plea for assessment environments which offer rich opportunities for students to “do” mathematics and for test designers to design rich items; automated scoring also needs further development, with respect to the scoring of intermediate steps in problem-solving strategies.