Moment problem is a classical question in real analysis, which asks whether a set of moments can be realized as integration of corresponding monomials with respect to a Borel measure. Truncated moment problem asks the same question given a finite set of moments. I will explain how some of the fundamental results in the truncated moment problem can be proved (in a very general setting) using elementary convex geometry. No familiarity with moment problems will be assumed. This is joint work with Larry Fialkow.