  A Hamiltonian two-field gyrofluid model is used to investigate the dynamics
of an electron-ion collisionless plasma subject to a strong ambient magnetic
field, within a spectral range extending from the magnetohydrodynamic (MHD)
scales to the electron skin depth. This model isolates Alfv\'en, Kinetic
Alfv\'en and Inertial Kinetic Alfv\'en waves that play a central role in space
plasmas, and extends standard reduced fluid models to broader ranges of the
plasma parameters. Recent numerical results are reviewed, including (i) the
reconnection-mediated MHD turbulence developing from the collision of
counter-propagating Alfv\'en wave packets, (ii) the specific features of the
cascade dynamics in strongly imbalanced turbulence, including a possible link
between the existence of a spectral transition range and the presence of
co-propagating wave interactions at sub-ion scales, for which new simulations
are reported, (iii) the influence of the ion-to-electron temperature ratio in
two-dimensional collisionless magnetic reconnection. The role of electron
finite Larmor radius corrections is pointed out and the extension of the
present model to a four-field gyrofluid model is discussed. Such an extended
model accurately describes electron finite Larmor radius effects at small or
moderate values of the electron beta parameter, and also retains the coupling
to slow magnetosonic waves.
