The subject invention concerns compounds having activity as inhibitors of proteasomes and methods of using the subject compounds. In one embodiment, a compound of the invention has the chemical structure shown in formula I: wherein R1 is an organic cyclic ring structure bonded to a sulfonamide structure; R2 is H, halogen, alkyl, —NR6R7, or heteroalkyl; R3 is H, halogen, —OH, —O-alkyl, alkyl, cycloalkyl, heterocycloalkyl, aryl, heteroaryl, —NO2, —NH2 or substituted amines; R4 is H, alkyl, heteroalkyl, aryl, or heteroaryl, any of which can be optionally substituted with one or more of —NO2, alkyl, heteroalkyl, aryl, or heteroaryl, or halogen; R5 is H, —OH, halogen, alkyl, aryl, heteroaryl, cycloalkyl, heterocycloalkyl, —O-alkyl, —O-aryl, heteroalkyl, —NO2, —NH2, or substituted amine; and R6 and R7 are independently H, O, alkyl, aryl, heterocycloalkyl, or heteroaryl, or together can form a heterocycloalkyl or a heteroaryl, any of which can be optionally substituted with one or more of —NO2, alkyl, heteroalkyl, aryl, or halogen; or a pharmaceutically acceptable salt or hydrate thereof. In another embodiment, a compound of the invention has the chemical structure shown in formula II: wherein Q, W, X, Y, Z are each independently carbon, oxygen, or nitrogen; R1 is H, or X1R8; R2 is heteroalkyl, which can be optionally substituted with one or more of —OH, halogen, —C(O)OR4, alkyl, heteroalkyl, heterocycloalkyl, or heteroaryl; R3 is heterocycloalkyl, aryl, heteroaryl, any of which can be optionally substituted with one or more of a halogen or —OH; and R4 is H or alkyl; R5 is halogen, alkyl or nitro; R6 is nitro, X2R9 or a halogen; R7 is H or alkyl; R8 is H, alkyl, aryl, CH2-alkyl-aryl, -alkyl-C(O)OH, or alkyl-tetrazole (aromatic and aliphatic heterocyclic groups); R9 is H or alkyl; X1 is oxygen, nitrogen, or sulfur; X2 is oxygen, nitrogen, or sulfur; or a pharmaceutically acceptable salt or hydrate thereof.