This paper provides some recent results obtained in the development of Immersed Boundary (IB) methods at the Politecnico di Bari: in particular, the development and testing of one such method—using a versatile Moving Least Squares approach, coupled with a very efficient solver for solving fluid-structure interaction problems in incompressible laminar flows—will be addressed. Such a method allows one to solve complex three-dimensional solid-fluid interaction problems within reasonable computer times. The solver is validated versus: the free fall of a sphere within a fluid at rest and jellyfish propulsion. Such results demonstrate the accuracy, efficiency, and versatility of the proposed method.