  This thesis consists of four parts. In the first part of the thesis, we
investigate the phase structure of Einstein-Maxwell-Scalar system with a
negative cosmological constant. We chart out the full phase diagram, and
discuss it's dependence on the value of the scalar charge. In the second part,
we do a systematic study of the phases of gravity coupled to an electromagnetic
field and charged scalar in flat space, with box boundary conditions, and we
show that the system admits both boson stars as well as hairy black holes as
solutions, providing yet another way to evade flat space no-hair theorems. In
part three, we explicitly diagonalize the simplest non-trivial Gurau-Witten
tensor model and study its spectral and late-time properties. We find parallels
to (a single sample of) SYK where some of these features were recently
attributed to random matrix behavior and quantum chaos. In particular, after a
running time average, the spectral form factor exhibits striking qualitative
similarities to SYK. In part four, we construct general asymptotically
Klebanov-Strassler solutions of a five dimensional $SU(2) \times SU(2) \times
\mathbb{Z}_2\times \mathbb{Z}_{2R}$ truncation of IIB supergravity on $ T^{1,1}
$, that break supersymmetry. We observe that there are only two SUSY-breaking
modes even in this generalized set up, and by holographically computing Ward
identities, we confirm that only one of them corresponds to spontaneous
breaking: this is the mode triggered by smeared anti-D3 branes at the tip of
the warped throat. Our results strengthen the evidence that {\it if} the KKLT
construction is meta-stable, it is indeed a spontaneously SUSY-broken (and
therefore bona fide) vacuum of string theory.
