Inflation provides the most theoretically attractive and observationally successful cosmological scenario able to generate the initial conditions of our Universe, while solving the standard cosmological problems. In this talk I will review the inflationary mechanism in its single-field slow-roll realization. In the first part I will describe the theoretical and mathematical aspects that lead to the observables we can measure in the present days in oder to test inflation, and also I will present the current status of the most favoured single-field inflationary models. In the second part I will talk particularly about the non-minimally coupled chaotic model as well as two model independent approaches of inflation.