Low-mass stars (<2–2.5 M๏) 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 review canonical evolution along the RGB and compare the classicle predictions of the so-called 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 nonstandard and shallow mixing process that changes the surface abundances at the so-called RGB bump. We discuss the current understanding of the connection between this extra-mixing and stellar rotation and conclude on the remaining open questions.