This thesis examines various properties of galaxies and clusters within hierarchical models of structure formation. A simple model based on analytical scaling relations is applied to X-ray observations of clusters at low and high redshift, in an attempt to constrain cosmological parameters from their evolutionary properties. It is found that the density parameter, Ωo cannot be constrained using the data alone. Two independent constraints on the slope of the linear power spectrum, infer values of Ωo < 0.7 at 95 per cent confidence. The remainder of this thesis concentrates on the method of cosmological simulation, a self- consistent approach to the modelling of structure in the Universe. A parameter-space study is performed for the simplest model of galaxy formation: the radiative cooling of baryons within the cores of dark matter haloes. It is found that the properties of the galaxies in the simulations are insensitive to the range of parameters studied, with the exception of those that affect the cooling rate of the gas. For modest resolution and reasonable choices of physical parameters, the amount of baryons in galaxy material is around a factor of 2 too high. An investigation is then performed for including the effects of star formation and energy from supemovae (feedback) within cosmological simulations, to reduce the amount of gas that cools. The star formation rate is driven by the minimum density for which the stars formation occurs and, for high star formation efficiencies, is limited by the cooling rate of the gas. A successful model for feedback is found to require the prevention of reheated gas from cooling for a short period of time, as an attempt to mimick the properties of a multiphase medium. Finally, preliminary results are presented for simulations of a galaxy cluster, including the effects of radiative cooling, star formation and feedback. The properties of the cluster are found to vary significantly between models with and without feedback, due to the feedback reducing the star formation rate by reheating gas that cools.