  We present two types of obstacles for constructing de Sitter space in
supersymmetric theories that appear as effective theories of quantum gravity.
The first obstacle concerns de Sitter critical points in extended supergravity
with charged massless gravitini. We show that all such critical points have a
Hubble scale of the same order or above the UV cutoff dictated by the magnetic
Weak Gravity Conjecture. The second obstacle concerns the dynamics of the
goldstino in models with non-linearly realized supersymmetry, such as string
models involving anti-branes. We show, using an exact renormalization group
approach, that the goldstino sector has an instability toward the formation of
condensates, which may have important qualitative consequences for de Sitter
constructions involving anti-brane uplifts.
