We review the main aspects of the warm inflation scenario, focusing on the
inflationary dynamics and the predictions related to the primordial spectrum of
perturbations, to be compared with the recent cosmological observations. We
study in detail three different classes of inflationary models, chaotic, hybrid
models and hilltop models, and discuss their embedding into supersymmetric
models and the consequences for model building of the warm inflationary
dynamics based on first principles calculations. Due to the extra friction term
introduced in the inflaton background evolution generated by the dissipative
dynamics, inflation can take place generically for smaller values of the field,
and larger values of couplings and masses. When the dissipative dynamics
dominates over the expansion, in the so-called strong dissipative regime,
inflation proceeds with sub-planckian inflaton values. Models can be naturally
embedded into a supergravity framework, with sugra corrections suppressed by
the Planck mass now under control, for a larger class of K\"ahler potentials.
In particular, this provides a simpler solution to the "eta" problem in
supersymmetric hybrid inflation, without restricting the K\"ahler potentials
compatible with inflation. For chaotic models dissipation leads to a smaller
prediction for the tensor-to-scalar ratio and a less tilted spectrum when
compared to the cold inflation scenario. We find in particular that a small
component of dissipation renders the quartic model now consistent with the
current CMB data.Comment: 22 pages, 5 figure
