  In this article we survey all known optimal isosystolic inequalities on
two-dimensional Finsler tori involving the following two central notions of
Finsler area: the Busemann-Hausdorff area and the Holmes-Thompson area. We also
complete the panorama by establishing the following new optimal isosystolic
inequality that is deduced from prior work by Burago and Ivanov: the
Busemann-Hausdorff area of a Finsler reversible $2$-torus with unit systole is
at least equal to $\pi/4$.
