Contemporary experiments prepare and probe quantum superpositions in increasingly macroscopic and complex many-body systems subject to environmental interactions. Motivated by the fact that quantum systems with a large number of interacting constituents are often described in the framework of quantum field theory, in this thesis a minimal and generic field-theoretic model is developed, that appropriately accounts for the decoherence dynamics towards a corresponding classical field theory. The main result is a generic Markovian master equation that induces the gradual classicalization of non-relativistic bosonic quantum fields in one spatial dimension. It turns any quantum superposition of distinct field configurations into a mixture, while ensuring that the expectation values of the canonical field variables evolve according to the classical field equations. Once the quantum coherences have decayed considerably, the semiclassical field dynamics is indistinguishable from a classical linear Boltzmann-type equation in the functional phase space of field configurations. The effect of the master equation on the field is minimal in the sense that it leaves the first moments of the mode quadratures unaffected, while increasing the field energy with a small state-independent rate. Assuming that the initial state of the field is a superposition of single-mode coherent states, several analytical expressions for the purity are obtained, which are in remarkable agreement with numerical calculations. The latter are carried out using quasi-Monte Carlo integration based on generalized Faure sequences. As established here, this is an efficient and accurate method for calculating expectation values in a high-dimensional quantum phase space. The presented results can be applied to a wide range of quantum many-body systems, and they set the stage for generalizations to tensorial fields in higher spatial dimensions and relativistic quantum fields.