  This thesis explores topics related to the study of quantum gravity, with a
focus on precision holography and higher-derivative supergravity. First, we
study subleading corrections to the free energy of a particular 3D N=3
Chern-Simons-matter theory found by Gaiotto and Tomasiello, which is given by a
matrix model after supersymmetric localization. This theory is dual to massive
IIA supergravity on AdS4, and consequently, the structure of subleading
corrections to the field theory naturally elucidates the higher-derivative
corrections to the gravity dual. We extract the first order of corrections to
the free energy using resolvent methods, and our results imply that particular
terms in the supergravity action should vanish on-shell. Next, we consider the
unreasonable effectiveness of five-dimensional minimal gauged supergravity.
There are three independent supersymmetric four-derivative terms that one can
add to the action; nevertheless, after going on-shell (or, equivalently, after
a field redefinition that pushes the off-shell discrepancies to six-derivative
order), there is a unique supersymmetric invariant. Third, we consider the
effect of higher-derivative corrections in holographic renormalization group
flows across dimensions. In particular, we construct a local holographic
c-function out of metric functions and show its monotonicity via the Null
Energy Condition. We also construct a c-function from the entanglement entropy
for flows with a CFT2 IR fixed point, and we show that such flows are
monotonic. Finally, we consider consistent truncations of four-derivative
heterotic supergravity. In particular, we show that reducing both on a torus
$T^n$ or on $S^3$ and truncating the vector multiplets is indeed a consistent
truncation at the four-derivative level. Moreover, we find examples of
two-derivative consistent truncations which fail to extend to four-derivative
ones.
