  In this thesis we give a pedagogical introduction to the construction of
NS5-D6(-O6)-D8(-O8) brane setups in massive type IIA string theory and the
six-dimensional $(1,0)$ SCFT's they engineer. After describing how to introduce
the various ingredients (and their interplay) in type IIA, we explain how to
read off an effective linear quiver description of the SCFT's from the brane
setups. We then explain in detail how to construct all AdS$_7$ solutions of
massive IIA supergravity which are dual to the field theories. We do this by
exploiting the power of generalized complex geometry. We then show how to
establish a holographic dictionary between four-dimensional $\mathcal{N}=1$
compactifications on a Riemann surface (without punctures) of the $(1,0)$
SCFT's and a certain class of massive IIA AdS$_5$ solutions, which are in
one-to-one correspondence with the AdS$_7$ vacua. We provide evidence for the
advocated AdS$_7$/CFT$_6$ and AdS$_5$/CFT$_4$ dualities by computing the
(leading order of the) field theory $a$ conformal anomaly from supergravity.
Finally, we briefly touch upon the construction of five-dimensional
$\mathcal{N}=1$ SCFT's through fivebrane webs, and reduce the classification
problem of their type IIB AdS$_6$ duals to a system of two coupled PDEs.
