Novel cyclic peptides, cyclic peptide conjugates and compositions containing them for treating neurological diseases in a subject include an Odorranalectin (OL) sequence or modified OL sequence as a scaffold and a biologically active peptide or protein and/or therapeutic agent conjugated thereto. Methods of treatment of neurological diseases are based on intranasal delivery of a cyclic peptide or cyclic peptide conjugate as described herein. Combinatorial libraries that include a plurality of cyclic peptides have also been developed and can be used to screen for a ligand(s) for a receptor of interest.