We consider the observational constraints on stupendously large black holes (SLABs) in the mass range $M gtrsim 10^{11},M_{odot}$. These have attracted little attention hitherto and we are aware of no published constraints on a SLAB population in the range $(10^{12}$ - $10^{18}),M_{odot}$. However, there is already evidence for black holes of up to nearly $10^{11},M_{odot}$ in galactic nuclei, so it is conceivable that SLABs exist and they may even have been seeded by primordial black holes. We focus on limits associated with (i) dynamical and lensing effects, (ii) the generation of background radiation through the accretion of gas during the pregalactic epoch, and (iii) the gamma-ray emission from the annihilation of the halo of weakly interacting massive particles (WIMPs) expected to form around each SLAB if these provide the dark matter. Finally, we comment on the constraints on the mass of ultra-light bosons from future measurements of the mass and spin of SLABs.
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