I will briefly describe our attempts to build a viable model of slow-roll inflation in the context
of Supergravity. In order to do that I first have to review the topic of moduli stabilisation and
the need to use D-term uplifting to generate a realistic de Sitter or Minkowski vacuum. The bottom
line is that, in order to comply with WMAP constraints a certain degree of fine-tuning is always
required. On the other hand, the fact that we can already link moduli from realistic string
compactifications with inflationary dynamics indicates that substantial progress in the field of
Particle Cosmology is being achieved.