This edited volume presents applications and modelling as a world-renowned sub-field of research in mathematics education. It includes the discussion on students' development of modelling competency through the teaching of applications and modelling. The teaching of mathematical modelling is considered from different perspectives, such as mathematical, pedagogical-didactical perspectives and critical-societal or socio-political perspectives. Assessment practices (local, regional or international) of modelling activities and difficulties with modelling activities at school and university levels, respectively, are discussed. Use of technology and other resources in modelling activities and their impact on the modelling processes are included in the considerations. Teaching practices, teacher education and professional development programs concerning the integration of applications and modelling in school and university mathematics programs are developedin this context.