The gauge/gravity duality has proven to be a very useful tool in the understanding of quantum field theories outside the perturbative regime. In particular, holography has been able to shed light not only on generic mechanisms of strongly coupled theories, but also on processes occurred in experimental set-ups, such as the heavy ion collisions. Experimental observations such as small viscosities or fast hydrodynamization find a natural explanation when the problem is expressed in terms of gravity and black holes. Despite the successes, however, it is important to bear in mind that holography provides computational tools for toy models rather than for QCD itself, and that these models are usable only under certain assumptions. Nature is very often far more nuanced than the models physicists use to describe it. In the case of heavy ion experiments and QCD there are many features that are commonly coarse grained in the holographic computations. For instance, non-trivial RG flows or baryon currents have not been included in the holographic models until very recently, although these are very relevant to experiments, and fundamental in critical phenomena. In this thesis we present a series of works in the topics field theory and heavy ion collisions that use applied holography and numeric GR as computational tools. The unifying factor among them is that they consider gravitational set-ups beyond pure gravity to describe the physics of conserved currents, non-trivial RG flows and phase transitions. In chapter 2 we use an Einstein-Maxwell set-up to compute the collision of two shock-waves with a conserved current and the hydrodynamization of the subsequent plasma. This conserved current is used to model the baryonic charge deposition by rapidity, observed in the experiments. The simulations are done with and without including the backreaction of the Maxwell field into the metric, which corresponds to the quenched approximation for the effects of the baryon charge on the gluons. In chapter 3 we present a one parameter family of non-conformal models. By adding an scalar field with a polynomial potential to the pure gravity set-up, we can achieve a non-trivial RG flow between two fixed points in the dual field theory. In this work we compute the thermodynamics and the quasi-normal modes spectra for the homogeneous states, being the latter one of the main results of the chapter. In chapter 4 we present the first holographic shock-wave collisions in a non-conformal model. To do so, we use the model introduced in chapter 3. In non-conformal models the average pressure in equilibrium is not fixed by symmetry, but by the equation of state. Out of equilibrium the average pressure might take any value, giving a new probe for the equilibration of the system. When the plasma's average pressure is well approximated by the equation of state value, we say that the system has “EoSizied”. In this chapter we show that the EoSization can indeed happen before the plasma has hydrodynamized. Finally, in chapter 5 we explore a holographic model that can contain phase transitions. This model is the same as the one presented in chapter 3, but now taking pure imaginary numbers for the controlling parameter. In an effort to understand the instabilities present in models with phase transitions, we trigger and evolve a spinoidal instability to its inhomogeneous end state. This is done by adding a small perturbation to a uniform black brane in a locally unstable branch, triggering a Gregory-Laflamme type instability in the gravity side. The most remarkable result found in the simulation is that both the evolution and the final result are well described by second order hydrodynamics.