  For decades, frustrated quantum magnets have been a seed for scientific
progress and innovation in condensed matter. As much as the numerical tools for
low-dimensional quantum magnetism have thrived and improved in recent years due
to breakthroughs inspired by quantum information and quantum computation,
higher-dimensional quantum magnetism can be considered as the final frontier,
where strong quantum entanglement, multiple ordering channels, and manifold
ways of paramagnetism culminate. At the same time, efforts in crystal synthesis
have induced a significant increase in the number of tangible frustrated
magnets which are generically three-dimensional in nature, creating an urgent
need for quantitative theoretical modeling. We review the pseudo-fermion (PF)
and pseudo-Majorana (PM) functional renormalization group (FRG) and their
specific ability to address higher-dimensional frustrated quantum magnetism.
First developed more than a decade ago, the PFFRG interprets a Heisenberg model
Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a
diagrammatic resummation scheme formulated as a renormalization group flow of
$m$-particle pseudofermion vertices. The article reviews the state of the art
of PFFRG and PMFRG and discusses their application to exemplary domains of
frustrated magnetism, but most importantly, it makes the algorithmic and
implementation details of these methods accessible to everyone. By thus
lowering the entry barrier to their application, we hope that this review will
contribute towards establishing PFFRG and PMFRG as the numerical methods for
addressing frustrated quantum magnetism in higher spatial dimensions.
