  Low mass stars (< 2-2.5 M_sun) exhibit, at all the stages of their evolution,
signatures of processes that require challenging modeling beyond the standard
stellar theory. In this paper we focus on their peculiarities while they climb
the red giant branch (RGB). We first compare the classical predictions for
abundance variations due to the first dredge-up with observational data in
various environments. We show how clear spectroscopic diagnostics probe the
nucleosynthesis and the internal mixing mechanisms that drive RGB stars.
Coherent data reveal in particular the existence of a non-standard mixing
process that changes their surface abundances at the so-called RGB bump. By
reviewing the models presented so far to explain the various abundance
anomalies, we show that the occurrence of this extra-mixing process is
certainly related to rotation. Finally we discuss the so-called Li-flash which
is expected to occur at the very beginning of the extra-mixing episode.
