We analyze models of primordial inflation with non-standard features. First, we study a model with an axion-type coupling between the inflaton and gauge fields. This sources an exponential growth of gauge fields during inflation. Considering the gauge field scattering rates we point out that this can lead to a thermal state during inflation, leading to a completely new regime, which leads to new observable consequences. We also study the evolution of this system when the inflaton is slowed down by dissipation of energy into gauge bosons instead of the usual Hubble friction: in particular we study the conditions of the onset of such a scenario from a static field configuration, its evolution and we mention some features which may arise in case of thermalization. Then, I analyse a second model of inflation, with a metastable vacuum which sources exponential inflation and we show that the presence of scalar-tensor gravity can induce a power-law expansion which allows successful tunneling. This model can have an observable feature: a peak of Gravitational waves at reheating. Finally we also analyze the case in which such a metastable vacuum might be in the Standard Model Higgs potential.