The present invention relates to peptides, in particular cell penetrating peptides, of 40 amino acid residues or less comprising at least one directly glycosylated amino residue and one or more arginine rich arm domains, and to conjugates of such cell penetrating peptides with a therapeutic molecule. The present invention further relates to the use of the peptides or conjugates in methods of treatment or as a medicament, especially in the treatment of genetic disorders of the central nervous system.