The present invention relates generally to the treatment of diseases and disorders that are mediated by histone deacetylase (HDAC), for example, cancer, with Belinostat (also known as (E)-N-hydroxy-3-(3-phenylsulfamoyl-phenyl)-acrylamide; PXD101; and PX 105684), and more particularly, to improvement treatments of such diseases (for example, cancers, for example, leukemias), which employ prolonged continuous infusion (e.g., prolonged continuous intravenous infusion) of Belinostat