Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established as the third pillar of discovery, alongside theory and experiment. Meanwhile, the performance of computing hardware grows through increasingly heterogeneous parallelism, enabling simulations of ever more complex models. However, efficiently implementing scalable codes on heterogeneous, distributed hardware systems becomes the bottleneck. This bottleneck can be alleviated by intermediate software layers that provide higher-level abstractions closer to the problem domain, reducing development times and allowing computational scientists to focus. Here, we present OpenFPM, an open and scalable framework that provides an abstraction layer for numerical simulations using particles and/or meshes. OpenFPM provides transparent and scalable infrastructure for shared-memory and distributed-memory implementations of particles-only and hybrid particle-mesh simulations of both discrete and continuous models, as well as non-simulation codes. This infrastructure is complemented with frequently used numerical routines, as well as interfaces to third-party libraries. We present the architecture and design of OpenFPM, detail the underlying abstractions, and benchmark the framework in applications ranging from Smoothed-Particle Hydrodynamics (SPH) to Molecular Dynamics (MD), Discrete Element Methods (DEM), Vortex Methods, stencil codes (finite differences), and high-dimensional Monte Carlo sampling (CMA-ES), comparing it to the current state of the art and to existing software frameworks. Program summary: Program Title: OpenFPM Program Files doi: http://dx.doi.org/10.17632/4yrp8nbm7c.1 Licensing provisions: GPLv3 Programming language: C++ Nature of problem: Writing numerical simulation programs that use meshes, particles, or any combination of the two typically requires long development times, in particular if the code is to scale efficiently on parallel distributed-memory computers. The long development times incur high financial and project-time costs and often lead to sub-optimal program performance as shortcuts are taken. Yet, a large portion of the functionality is common across programs and could be automated or provided as reusable software components, leading to large savings in project costs and potentially improved software performance. Solution method: OpenFPM provides a scalable, highly efficient software platform for numerical simulations using meshes, particles, or any combination of the two on parallel computers. It is based on a well-known set of abstract data types and operators that suffice to express any such simulation, regardless of the application domain. OpenFPM provides reusable, tested, and internally parallelized software components that reduce development times and make parallel computing accessible to computational scientists without extensive knowledge in parallel programming. Additional comments including restrictions and unusual features: OpenFPM is a software library based on which users can implement their simulation codes at a fraction of the development cost. All parallelization and memory handling is transparently done by the library. As its main innovation, OpenFPM makes use of C++ Template Meta Programming in order to enable simulations in arbitrary-dimensional spaces, distribution of arbitrary user-defined C++ objects, and compile-time code optimization and targeting for specific hardware platforms. OpenFPM-based simulations can directly output VTK files for visualization of results and HDF5 files for data archiving.