The demand for accurate solutions of increasingly complicated real-world problems means that the underlying data structures also become increasingly complicated. This is particularly evident with multi-physics, hp-adaptivity, and/or evolving geometries (e.g. crack propagation). Established commercial software is often limited in this respect, or can be relatively slow to adopt new innovations. Working around these problems has been the main motivation for the development of MoFEM, recognising that it is increasingly necessary for engineers, scientists and mathematicians to carry out calculations using several mesh refinements, different approximation orders, multiple degrees of freedom and/or different scales.