Geometry has been extensively studied for the past two centuries, almost exclusively from a differential point of view. With the advent of the digital age, this interest in differential geometry has now partially shifted, due to the growing importance of discrete geometry: from 3D surfaces in graphics to higher dimensional manifolds in mechanics, computational science now often has to deal with sampled geometric data on a daily basis. This is, of course, particularly true for computer graphics---hence our interest in applied geometry. In this talk we will argue that, for many problems in applied geometry, adopting a discrete variational formulation is preferable to blind discretizations of intrinsically-continuous formulations. We will show results of such a general approach for various applications, including parameterization, smoothing, approximation, as well as thin-shell simulation. A brief description of how these simple geometric concepts can be used to develop a discrete calculus of tensors and forms for other computational sciences (mechanics, electro-magnetism, etc) will conclude the talk.