Shape Modeling constitutes a fundamental problem in computer vision. Complexity of the problem arises from the variability of shape realizations, which may be due to their inherent variability or introduced because of adverse situations like noise, pose problem, occlusion, etc. In this thesis, we address this fundamental problem for 2D and 3D shapes in statistical as well as algorithmic settings. In a probabilistic setting, we present a novel method for 2D shape modeling and template learning, which we call Flexible Skew-symmetric Shape Model ($FSSM$). It uses an extended class of semiparametric skew-symmetric distributions. The proposed model aims at capturing the inherent variability of shapes so long as the realization contours remain within a certain neighborhood range around a 'mean' with high probability. It is flexible enough to capture the non-Gaussianity of underlying data, and allows automatic selection of landmarks. We explore several applications of $FSSM$, such as, sampling new shapes, learning templates, and classifying shapes. The algorithmic 2D and 3D shape models are formulated in a Morse theoretic framework, where shapes of arbitrary topology are represented completely by topo-geometric graphs. The idea is to capture topology by localizing critical points of distance function as the Morse function, thereby representing it through skeletal graphs. Geometry, on the other hand, is captured by tracking radii of the corresponding level curves of the distance function (for planar shapes), or by modeling the evolution of these level curves (for 3D shapes). This leads to a weighted skeletal representation, which is then employed for reconstruction, and recognition applications.