This paper reviews recent work by the authors on inflation in single-field models with noncanonical (higher-order) kinetic terms. Such terms arise naturally in an EFT approach to modelling inflation, and also from certain string theory embeddings, such as in DBI inflation. Theories containing such terms can support a period of noncanonical inflation which is smoothly connected to the usual slow-roll regime. We give a general formalism for finding solutions of the equations of motion corresponding to noncanonical inflation. However, not every Lagrangian with higher-power kinetic operators supports noncanonical inflation, and not every set of initial conditions in a suitable theory will give rise to an inflationary trajectory. We give some sufficient conditions required for a Lagrangian to support inflation in the non-canonical regime. Further, we investigate the problem of fine-tuning in these models. We find that noncanonical kinetic terms tend to reduce the severity of the fine-tuning problem in general, as long as a regime of noncanonical inflation is present.