The phenomenon of nozzle failure of an inkjet printhead due to entrainment of air bubbles was studies using analytical and numerical models. The studied inkjet printheads consist of many channels in which an acoustic field is generated to eject a droplet. When an air bubble is entrained, it disrupts the droplet formation process. This phenomenon is called nozzle failure. A very simple analytical model of a bubble in a nozzle was shown to qualitatively capture the dependence of the droplet velocity on the bubble volume. A more advanced model in which the two-way coupling between the channel acoustics and the bubble volume oscillations is taken into account, is shown to quantitatively agree with experimental data. The two-way coupling between bubble volume oscillations and channel acoustics is essential in this case. To determine when two-way coupling can be neglected, a complete set of dimensionless groups is derived. This set of dimensionless groups yields sharp criteria for the significance of two-wat coupling and for nonlinearity in the volume oscillations. A fully nonlinear numerical model is developed to test the predictions from the dimensionless groups. The predictions are confirmed by the results from the numerical model. This model is extended to also calculate the translational motion of the bubble and its growth by rectified diffusion. The effects that cause air entrainment were also studied. The outside of the printhead is coated by a thin ink film. This ink film flows whenever the printhead is actuated due to Marangoni stress. This flow is the first link in a chain of events that causes air entrainment. A careful analysis of the governing equations shows that these thin Marangoni flows satisfy potential flow. This result is used to analytically calculate the evolution of a moving droplet and a fingering instability, and the theoretical predictions are confirmed by the observations.