The present disclosure relates to polymers comprising conjugates of cyclodextrin or derivatives thereof and a linker moiety, and their application in treating lipid storage disorders by the removal of lipids such as cholesterol from cells. The polymers having the following structure: Formula (I), wherein CD, L, and n are defined herein, exhibit improved properties including but not limited to improved biocompatibility, improved retention time, prolonged duration of action in cells, and increased efficacy in treating a variety of kidney diseases and associated conditions.