The present invention relates generally to the treatment of diseases and disorders that are mediated by histone deacetylase (HDAC), for example, cancer, with Belinostat&trade (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&trade.