From spacecraft data, it is evident that electron pressure anisotropy develops in collisionless plasmas. This is in contrast to the results of theoretical investigations, which suggest this anisotropy should be limited. Common for such theoretical studies is that the effects of electron trapping are not included; simply speaking, electron trapping is a non-linear effect and is, therefore, eliminated when utilizing the standard methods for linearizing the underlying kinetic equations. Here, we review our recent work on the anisotropy that develops when retaining the effects of electron trapping. A general analytic model is derived for the electron guiding center distribution (v∥,v⊥)
of an expanding flux tube. The model is consistent with anisotropic distributions observed by spacecraft, and is applied as a fluid closure yielding anisotropic equations of state for the parallel and perpendicular components (relative to the local magnetic field direction) of the electron pressure. In the context of reconnection, the new closure accounts for the strong pressure anisotropy that develops in the reconnection regions. It is shown that for generic reconnection in a collisionless plasma nearly all thermal electrons are trapped, and dominate the properties of the electron fluid. A new numerical code is developed implementing the anisotropic closure within the standard two-fluid framework. The code accurately reproduces the detailed structure of the reconnection region observed in fully kinetic simulations. These results emphasize the important role of pressure anisotropy for the reconnection process. In particular, for reconnection geometries characterized by small values of the normalized upstream electron pressure, βe∞
, the pressure anisotropy becomes large with p∥≫p⊥
and strong parallel electric fields develop in conjunction with this anisotropy. The parallel electric fields can be sustained over large spatial scales and, therefore, become important for electron acceleration.