Radiative stability represents a crucial requirement for any viable model of inflation. With this in mind, I will review the current status of inflationary model building. I will focus especially on axion-like particles known as pseudo-Nambu-Goldstone bosons (pNGBs), that provide a major candidate in this context. After discussing the observational status of pNGB-driven inflation, I will illustrate the difficulties one faces when trying to embed these models in string theory. In the second part of the talk I will show how a pNGB can get a radiatively stable, quadratic potential (aka chaotic inflation) in theories where it mixes with a 4-form field, and how such a mixing is naturally present in string theory.