The work carried out during this Thesis is framed within the field of Numerical Cosmology and focused on several broad lines intimately related which deal with the theoretical and numerical study of galaxy clusters: (i) the halo-finding problem, (ii) new improvements in cosmological simulations, and (iii) the formation and evolution of galaxy clusters. In spite of the achievements reached by Computational Cosmology in the last years, present-day hydrodynamics/N-body simulations still present important discrepancies with the observations, especially in the inner regions of massive galaxy clusters. Among these discrepancies we can cite, for instance, the breaking up of the self-similar scaling relations or the cooling flow problem. These discrepancies have motivated the idea that, besides gravity and adiabatic gas dynamics, non-gravitational processes related with the baryonic component of the Universe need to be included in our simulations. Within this context, in a complementary way to the different non-gravitational processes being included in simulations, it is crucial to properly describe different gravitational processes inherent to the hierarchical formation of cosmic structures itself. In this sense, the objective of the present work is to describe, in a consistent way, some of the heating processes associated with the hierarchical evolution of galaxy clusters in a full cosmological context. To identify the different cosmological structures and analyse their evolutionary histories, an Eulerian cosmological code and a grid-based halo finder have been used. The cosmological code used during this Thesis, MASCLET (Quilis, 2004), is an Eulerian code based on an adaptive mesh refinement (AMR) scheme able to model the coupled evolution of the dark matter and the baryonic components of the Universe. To analyse the outputs of these complex simulations, a new halo finder based on the spherical overdensity method (SO) has been developed (ASOHF, Planelles & Quilis, 2010). This finder allows us to extract the dark matter haloes (numerical counterpart of galaxies and galaxy clusters) and analyse, in a precise way, their main physical properties. Making use of these numerical tools, MASCLET and ASOHF, the role played by galaxy cluster mergers, as well as by the cosmological shock waves developed during these events, as sources of heating of the intracluster medium (ICM) has been analysed in a full cosmological context. In order to do so, two simulations have been performed with the MASCLET code. In these simulations, the unique relevant feedback mechanism considered is the gravitational, that is, the inherent to the hierarchical evolution of the Universe. Analysing these simulations it has been demonstrated that galaxy cluster mergers and cosmological shock waves play a crucial role, not only on galaxy cluster properties, but on the thermalization of the ICM. In particular, it has been demonstrated that galaxy cluster mergers have a direct influence on the existence of cool cores in the centre of massive galaxy clusters as well as on the scatter observed in the self-similar scaling relations (Planelles & Quilis, 2009). On the other hand, shock waves are also crucial in galaxy cluster properties contributing very efficiently to the virialization of haloes and the thermalization of the Universe. Moreover, it has been observed that the strength of shocks within the virial radius of galaxy clusters shows some correlation with their virial masses, being directly related with their dynamical histories.La presente Tesis se centra en varias líneas de investigación íntimamente relacionadas que tratan con el estudio teórico y numérico de los cúmulos de galaxias: (i) el problema de encontrar los halos de materia oscura, (ii) nuevas mejoras en simulaciones cosmológicas y, (iii) la formación y evolución de los cúmulos de galaxias. Las simulaciones hidrodinámicas/N-cuerpos actuales todavía presentan importantes discrepancias con las observaciones, especialmente en las regiones internas de los cúmulos de galaxias más masivos. Entre estas discrepancias podemos citar, por ejemplo, la ruptura de las relaciones de la escala auto-semejantes o el problema de los flujos de gas frío. Estas discrepancias han motivado la idea de que, además de gravedad y dinámica de gases adiabática, procesos no gravitacionales relacionados con la componente bariónica del Universo deben ser incluidos en las simulaciones. En este contexto, de forma complementaria a diferentes procesos no gravitacionales, es crucial describir de forma adecuada los distintos procesos gravitacionales inherentes a la propia formación jerárquica de la estructuras cósmicas. En este sentido, el objetivo del presente trabajo es describir, de forma auto-consistente, algunos de los procesos de calentamiento asociados a la propia evolución jerárquica de los cúmulos de galaxias en un contexto puramente cosmológico. Para ello, se ha hecho uso de un código cosmológico euleriano (MASCLET, Quilis, 2004) y un buscador de halos basado en el método de sobredensidad esférica (ASOHF, Planelles y Quilis, 2010). Haciendo uso de estos códigos, se ha analizado el papel que juegan las fusiones de cúmulos de galaxias y las ondas de choque generadas durante estos eventos como fuentes de calentamiento del medio intracúmulo en un contexto puramente cosmológico. En este sentido, se ha comprobado que las fusiones de cúmulos de galaxias influyen directamente en la existencia de núcleos fríos en el centro de los cúmulos más masivos, así como en la dispersión observada en las relaciones de escala auto-semejantes (Planelles y Quilis, 2009). Por otra parte, también se ha comprobado que las ondas de choque contribuyen eficientemente a la virialización de los halos y a la termalización del Universo.