To solve complex engineering problems, among the different numerical methods recently proposed in the literature, Lagrangian Approaches, based on the Particle Finite Element Method (PFEM), are gaining more and more attention. The PFEM is a mesh-based Lagrangian method for fluid modelling, particularly suited for problems with large changes in the domain topology. The Lagrangian nature of the approach allows for a natural treatment of free surfaces undergoing large displacements and of fast-evolving interfaces, making the method particularly suitable for engineering applications. To avoid the excessive distortion of the mesh, typical of Lagrangian approaches for fluids, the method uses a continuous remeshing, based on a fast and efficient Delaunay triangulation. Moreover, a 3D version of the alpha-shape technique is used to define the position and the evolution of the free surfaces. Special attention is devoted to the boundary conditions. In some special cases, like inflow, outflow or slip, boundary conditions can be complex to be imposed in a standard Lagrangian approach and consequently, a mixed Lagrangian-Eulerian technique has been developed. The proposed approach has been validated and used to solve different non-Newtonian fluid flow problems, e.g flow of fresh concrete, movements of pipelines in liquefied sand, dynamics analysis of granular material or 3D printing. In the present work, an overview of the proposed technique and its applications in different engineering problems will be given.