A cycloazapeptide of the formula Z: wherein: each Q 1, Q 2, Q 3, Q 4 and Q 5 is independently -CH- or N, provided that at least one of Q 1, Q 2, Q 3, Q 4 and Q 5 is N; R 1 is hydrogen or is selected from the group consisting of a side chain of a natural amino acid and a side chain of an unnatural amino acid; R 2 and R 3 are each independently selected from the group consisting of -H, C 1 -C 6 alkyl, C 2 -C 6 alkenyl, C 2 -C 6 alkynyl, C 1 -C 6 alkyloxy, C 1 -C 6 alkoxyalkyl, aryl, aryl-(C 1 -C 6 alkylene)-, 3- to 7-membered carbocycle, 3- to 7-membered heterocycle, hydroxy-C 1 -C 6 -alkyl and C 1 -C 6 -alkoxy-C 1 -C 6 -alkyl, wherein the alkyl, alkenyl, alkynyl, alkyloxy, alkoxyalkyl, aryl, carbocycle and heterocycle groups are each optionally substituted; R 7 is absent or is selected from the group consisting of H, C 1 -C 6 alkyl, C 2 -C 6 alkenyl, C 2 -C 6 alkynyl, aryl, aryl-(C 1 -C 6 alkylene)-, a 3- to 7-membered carbocycle, and a 3- to 7-membered heterocycle, wherein the alkyl, alkenyl, alkynyl, aryl-alkylene, carbocycle and heterocycle groups are each optionally substituted; wherein R 2, R 3 and R 7 are not all H; R 8 is hydrogen or is selected from the group consisting of a side chain of a natural amino acid and a side chain of an unnatural amino acid; X is a 5 or 6-membered heterocycle or a linker comprising a hydrophilic moiety selected from the group consisting of hydroxyl, carbonyl, amide (-C NH-), sulfonamide, sulfonate, phosphate, polar amino acid moiety, PEG moiety, carbocycles or heterocycles substituted with at least one hydroxyl group and sugar moiety, or a combination thereof; Y is a 5 or 6-membered heterocycle or a linker comprising a hydrophilic moiety selected from the group consisting of hydroxyl, carbonyl, sulfonamide, sulfonate, phosphate, polar amino acid moiety, PEG moiety, carbocycles or heterocycles substituted with at least one hydroxyl group and sugar moiety; where at least one of X and Y is a 5 or 6-membered heterocycle; and w is 1, 2, 3, 4 or 5; or a pharmaceutically acceptable salt thereof, optionally in the form of a single stereoisomer or mixture of stereoisomers thereof. each Q 1, Q 2, Q 3, Q 4 and Q 5 is independently -CH- or N, provided that at least one of Q 1, Q 2, Q 3, Q 4 and Q 5 is N; R 1 is hydrogen or is selected from the group consisting of a side chain of a natural amino acid and a side chain of an unnatural amino acid; R 2 and R 3 are each independently selected from the group consisting of -H, C 1 -C 6 alkyl, C 2 -C 6 alkenyl, C 2 -C 6 alkynyl, C 1 -C 6 alkyloxy, C 1 -C 6 alkoxyalkyl, aryl, aryl-(C 1 -C 6 alkylene)-, 3- to 7-membered carbocycle, 3- to 7-membered heterocycle, hydroxy-C 1 -C 6 -alkyl and C 1 -C 6 -alkoxy-C 1 -C 6 -alkyl, wherein the alkyl, alkenyl, alkynyl, alkyloxy, alkoxyalkyl, aryl, carbocycle and heterocycle groups are each optionally substituted; R 7 is absent or is selected from the group consisting of H, C 1 -C 6 alkyl, C 2 -C 6 alkenyl, C 2 -C 6 alkynyl, aryl, aryl-(C 1 -C 6 alkylene)-, a 3- to 7-membered carbocycle, and a 3- to 7-membered heterocycle, wherein the alkyl, alkenyl, alkynyl, aryl-alkylene, carbocycle and heterocycle groups are each optionally substituted; wherein R 2, R 3 and R 7 are not all H; R 8 is hydrogen or is selected from the group consisting of a side chain of a natural amino acid and a side chain of an unnatural amino acid; X is a 5 or 6-membered heterocycle or a linker comprising a hydrophilic moiety selected from the group consisting of hydroxyl, carbonyl, amide (-C NH-), sulfonamide, sulfonate, phosphate, polar amino acid moiety, PEG moiety, carbocycles or heterocycles substituted with at least one hydroxyl group and sugar moiety, or a combination thereof; Y is a 5 or 6-membered heterocycle or a linker comprising a hydrophilic moiety selected from the group consisting of hydroxyl, carbonyl, sulfonamide, sulfonate, phosphate, polar amino acid moiety, PEG moiety, carbocycles or heterocycles substituted with at least one hydroxyl group and sugar moiety; where at least one of X and Y is a 5 or 6-membered heterocycle; and w is 1, 2, 3, 4 or 5;