  This thesis deals with applications of holographic dualities to the study of
background field and time dependence effects in strongly coupled field
theories.
  The first chapters (2-5) aim to provide a self-contained review of the
Sakai-Sugimoto model (SSM) as a top-down approach to holographic QCD,
introducing first the necessary background on QCD, string theory and AdS/CFT.
Chapter 7 reviews finite temperature holography, to be used in the subsequent
chapters.
  We use the non-Abelian ($N_f = 2$) SSM to study a possible magnetically
induced instability of the QCD vacuum towards a superconducting phase, as
previously discussed in phenomenological QCD models and there referred to as
"rho meson condensation". We find that this instability can indeed be
holographically described by the SSM, and obtain increasingly higher
predictions for the necessary critical magnetic field in increasingly
complicated (i.e. less simplified) set-ups. The obtained results are presented
in chapter 6 and are based on arXiv:1105.2217 and arXiv:1309.5042. In chapter 8
we discuss the splitting of chiral transition temperatures per flavour in the
finite temperature regime of the $N_f = 2$ SSM, indicating an intermediate
phase where chiral symmetry is only partially restored. This was previously
presented in arXiv:1303.5674.
  In chapter 9, instead of a top-down approach, bottom-up models known as
"AdS-Vaidya" models are used in the context of condensed matter applications to
study far-from-equilibrium behaviour of strongly coupled electron systems. A
notion of a time-dependent spectral function is defined and calculated in
Reissner-Nordstr\"om-AdS$_4$-Vaidya as a very first step towards extracting in
principle measurable quantities in time-resolved ARPES experiments
[arXiv:1407.5975]. Focus is put on explaining the used numerical method
(pseudospectral method).
