Dynamics of nucleate boiling are strongly affected by the formation and behaviour of the microlayer, a layer of liquid underneath growing bubbles. As a result of its minute thickness, very high heat fluxes occur within the microlayer and its evaporation contributes significantly to the overall heat transfer. Microlayer formation is, however, not guaranteed and the transition from the contact-line to the microlayer regime of nucleate boiling is not fully understood. The difficulty of experimental investigation of the microlayer and the uncertainties surrounding its formation and subsequent evolution motivate the use of Direct Numerical Simulation (DNS) to model its behaviour. In this work, a computational strategy for utilising DNS to model nucleate boiling by resolving explicitly the microlayer is developed. The numerical method is based on the resolution of continuum conservation equations for incompressible two-phase flows in Cartesian and axisymmetric cylindrical coordinates. The phasic interface is tracked by means of the geometric Volume-of-Fluid (VOF) method and the algorithm is applicable both to adiabatic and volatile flows. Online, implicit coupling of the fluid and solid domains for the solution of the conjugate heat-transfer problem is included and closure models for the treatment of the interfacial heat-transfer resistance and the dynamic contact angle are introduced. A rigorous verification and validation exercise is performed to evaluate the efficacy of the numerical algorithm. Subsequently, a theoretical criterion for modelling the transition between contact-line and microlayer regimes is derived, and tested. Very good agreement is found with the reference experimental and simulation data and the predictive power of the criterion is demonstrated with the aid of DNS results. The computational procedure is then validated for simulations of nucleate boiling with resolved microlayer using relevant experimental data recently measured at the Massachusetts Institute of Technology; it is shown that the main observed growth features and surface heat-transfer characteristics are well-reproduced using the overall method. A sensitivity study of the dependence of the initial microlayer thickness on the growth conditions is performed and a universal equation describing the thickness distribution is proposed with liquid properties and bubble expansion rate being the governing parameters. Finally, the computational method is extended to coarse-mesh problems by introducing several reduced-order models and the full bubble-growth cycle from nucleation to detachment is simulated. Good agreement with reference measurements is again achieved and the experimental findings regarding the force balance during nucleate boiling are confirmed.