New competence-oriented learning goals can only be sustainably implemented if they are aligned with teaching and assessment goals. Within the fields of science, technology and mathematics education, one approach of compe-tence-oriented teaching is based on the concept of inquiry-based education. Scien-tific inquiry in science, problem solving in mathematics, design processes in tech-nology and innovation as a cross-curricular approach to teaching and learning that is emphasised as a key element of 21st century skills allow students to engage in the thinking and working processes of scientists. By applying these approaches, teachers can address subject-specific as well as generic competences (e.g. investi-gation in science as a subject-specific competence vs. argumentation or communi-cation as more generic competences). Since what is assessed strongly influences what is taught, changes in teaching need to be accompanied by changes in assess-ment in order to be sustainable. Teaching and learning goals need to be aligned and assessment methods developed that allow for the assessment of competences related to scientific inquiry, mathematical problem solving or design and innova-tion processes. This chapter aims to provide a short overview about these inquiry-based approaches in the teaching and learning of science, technology, mathematics and innovation. Following a short introduction, the chapter consists of four sub-sections devoted to scientific inquiry, mathematical problem solving, design pro-cesses and innovation. Each subsection addresses three basic questions: (1) How is the construct defined and conceptualized? (2) How does teaching for inquiry change teaching? (3) What changes in assessment are necessary to assess inquiry competences?