While Isogeometric Analysis (IGA) [1] has significantly impacted much of computational mechanics, one area that has benefited greatly from IGA research is computational methods for shell structures. Because geometrically complex, smooth surfaces are naturally represented in Computer-Aided Design (CAD) systems, much of that technology could be directly employed in the discretization of existing shell theories, with increased accuracy and robustness in general-purpose nonlinear applications relative to traditional Finite Element Analysis (FEA) representations. In addition, the increased smoothness of CAD surface representation (by means of B-Splines and their rational and unstructured variants) enabled the formulation, and use in general-purpose nonlinear applications, of thin shell theories. i.e., the Kirchhoff—Love (KL) shells, previously unattainable in traditional FEA. Meshfree methods were developed in the 90’s based on the concept of kernel estimation [2]. The meshfree approximation is developed directly using a collection of points scattered in space, i.e., the point cloud. The approximation does not require a mesh data structure and its’ order of accuracy and smoothness may be controlled independently. These attributes make meshfree methods highly effective for the simulation of materials and structures undergoing extreme deformations, including fracturing and fragmentation. The higher-order smoothness of meshfree methods also makes them excellent candidates for the discretization of KL shells. However, shell formulations require parameterization of the mid-surface geometry. While such parameterization is natural to FE and IGA, it’s not a straightforward task for meshfree methods. In this presentaion, we develop a modeling framework for KL shells treating them as 3D solids that are constrained to satisfy the KL shell kinematics. The resulting general-purpose formulation is amenable to a direct discretization using IGA, and is presented first [3]. To adapt the formualtion to a Meshfree framework, additional surface parameterization and stabilized nodal-intergation techniques are developed [4]. The theoretical and numerical formulations are augmented with advanced applications showing the accuracy, stability and practicality of the proposed KL shell modeling and simulation framework.