  This research chapter provides a comprehensive overview of ferromagnetic
gyroidal nanostructures, combining a review of state-of-the-art research with
our new findings on their implications for 3D magnonics. Both static and
dynamic magnetization studies show that non-trivial shape anisotropy,
chirality, and inhomogeneous demagnetization fields influenced by specific
crystallographic arrangements lead to multiple low-energy state magnetization
textures, spin-wave mode localization, and controllable spin-wave propagation,
highlighting the substantial potential of gyroidal nanostructures.
  The review integrates insights into micro/nano texturing to elucidate the
intricate relationships between gyroidal geometry, chirality, and their
effective magnetic properties, especially at microwave frequencies. Our study
of resonance frequencies in gyroid samples under rotational field manipulation
further reveals the significant influence of geometric anisotropy on
ferromagnetic resonance signal strength. This chapter establishes a fundamental
understanding of ferromagnetic gyroidal nanostructures, paving the way for
their future investigation in 3D magnonics.
