In inflationary theories, single field models are typically considered subject to slow-roll conditions. In this talk I will present current observational constraints on deviations from slow-roll, e.g. bounds coming from strong coupling considerations, scale-dependent non-Gaussianities and the tensor-to-scalar ratio. These constraints still allow significant violations of slow-roll conditions. Focusing on non-Gaussian signals, I will discuss a variety of intriguing observable signatures that can be found for fast-rolling single fields.