  We present the most comprehensive global fits to date of three supersymmetric
models motivated by grand unification: the Constrained Minimal Supersymmetric
Standard Model (CMSSM), and its Non-Universal Higgs Mass generalisations NUHM1
and NUHM2. We include likelihoods from a number of direct and indirect dark
matter searches, a large collection of electroweak precision and flavour
observables, direct searches for supersymmetry at LEP and Runs I and II of the
LHC, and constraints from Higgs observables. Our analysis improves on existing
results not only in terms of the number of included observables, but also in
the level of detail with which we treat them, our sampling techniques for
scanning the parameter space, and our treatment of nuisance parameters. We show
that stau co-annihilation is now ruled out in the CMSSM at more than 95\%
confidence. Stop co-annihilation turns out to be one of the most promising
mechanisms for achieving an appropriate relic density of dark matter in all
three models, whilst avoiding all other constraints. We find high-likelihood
regions of parameter space featuring light stops and charginos, making them
potentially detectable in the near future at the LHC. We also show that
tonne-scale direct detection will play a largely complementary role, probing
large parts of the remaining viable parameter space, including essentially all
models with multi-TeV neutralinos.
