The main chain of proline residues has a restricted conformational space with a far smaller range of allowed Phi/Psi angles than other amino acid have. In positions where the main-chain conformation is compatible with this allowed range, Pro can facilitate folding (e.g. in beta turns). In positions where a different main-chain conformation is required, a mutation to Proline can be highly destabilizing.
The main-chain amid nitrogen is part of the ring structure of proline and therefore cannot participate in hydrogen bonds. As a consequence, Pro destabilizes secondary structure elements such as helices and beta sheets, or causes kinks in a helix. It is often found at the ends of secondary structures.
Proline cis-trans isomerization can be limiting for folding kinetics.
Hydroxyproline plays an important role in stabilizing the collagen triple helix.
In addition to what is already indicated by Annemarie Honegger , multiple prolines and/or hydroxyprolines in a row can create a so-called polyProline helix (also known as an extended helix or PPII helix).
This is a known structure involved, as said, in the predominant secondary structure in collagen. The idea is that because of the ‘bulky’ side-chain an extended structure such as the polyProline helix is formed and not only for prolines but also observed for polyLysine when at a pH with multiple positive charges and other examples.
See for example:
Article Polyproline-II Helix in Proteins: Structure and Function
Chapter Characterization of helical junction zones in gelatin networ...
Chapter Characterization of helical structures in gelatin networks a...
Proline-rich sequences play a specific role in SH3-mediated protein-protein interactions, frequently seen in signal transduction cascades of tyrosine-kinase receptors and receptor-associated src-type kinases: SH3 domains bind proline-rich sequences, particularly those carrying the PxxP motif that have the left-handed polyproline 2 (PPII) conformation.
https://en.wikipedia.org/wiki/SH3_domain
Article SH3 domains: Modules of protein-protein interactions