  We study singularities of Lagrangian mean curvature flow in $\C^n$ when the
initial condition is a zero-Maslov class Lagrangian. We start by showing that,
in this setting, singularities are unavoidable. More precisely, we construct
Lagrangians with arbitrarily small Lagrangian angle and Lagrangians which are
Hamiltonian isotopic to a plane that, nevertheless, develop finite time
singularities under mean curvature flow.
  We then prove two theorems regarding the tangent flow at a singularity when
the initial condition is a zero-Maslov class Lagrangian. The first one (Theorem
A) states that that the rescaled flow at a singularity converges weakly to a
finite union of area-minimizing Lagrangian cones. The second theorem (Theorem
B) states that, under the additional assumptions that the initial condition is
an almost-calibrated and rational Lagrangian, connected components of the
rescaled flow converges to a single area-minimizing Lagrangian cone, as opposed
to a possible non-area-minimizing union of area-minimizing Lagrangian cones.
The latter condition is dense for Lagrangians with finitely generated
$H_1(L,\Z)$.
