The invention provides various novel compositions of berberine in combination with pharmacologically active organic acids, and related methods of their use in treating various diseases or disorders. The invention further provides various novel compounds prepared from berberine and pharmacologically active organic acids and prepared from ursodeoxycholic acid and pharmacologically active organic bases, and pharmaceutical compositions thereof, and methods of their preparation and therapeutic use in treating and / or preventing various diseases or disorders. The compounds and pharmaceutical compositions of the invention can be utilized to treat various diseases or disorders, such as diabetes, diabetic complications, dyslipidemia, hyperlipidemia, obesity, metabolic syndromes, pre-diabetes, atherosclerosis, heart diseases, neurodegenerative diseases, sarcopenia, muscle atrophy, inflammation, cancer and liver diseases and conditions such as fatty liver, non-alcoholic fatty liver disease, non-alcoholic steatohepatitis, cholestatic liver diseases or graft-versus-host disease of the liver. The compounds of this invention are also useful in improving liver functions in chronic viral associated liver diseases and alcohol-related liver diseases.