This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education courses and the role of interdisciplinary projects in teaching upper level calculus. Various problems and models that emphasize the geometric roots of mathematics, its connections to other disciplines, and relevance to the outside world have been presented as meaningful tools to stimulate students' intellectual curiosity and develop their self-confidence in the subject matter. Didactical significance of famous results is discussed. (Contains 4 figures.)