I will discuss string theory compactifications where a large number of moduli is stabilized by fluxes. I will present a conjecture which rules out the stabilization of all complex-structure moduli in F-theory at a generic point in moduli space by fluxes that satisfy the tadpole cancellation condition. Evidence for this conjecture comes from K3xK3 compactifications. Using evolutionary algorithms we found that moduli stabilization needs fluxes whose charge is slightly smaller than 1/2 of the number of moduli and larger than what is allowed by tadpole cancellation. I will furthermore comment on possible implications on de Sitter vacua obtained by antibrane uplift in long warped throats.