Gene expression is a finely tuned, intricate process that normally regulates cellular identity, and becomes disrupted in cancer. One class of molecules inside cells that contribute to gene expression are the so-called RNA binding proteins, defined as proteins whose function is to bind ribonucleic acids (RNA). These proteins participate in gene expression by regulating messenger RNA (mRNAs), which in turn are made into proteins. Some of these RNA binding proteins are known to play roles in cancers, and specifically in blood cancers. In this article, we examine the work of other scientists who have developed various ways to counteract the functions of these RNA binding proteins using chemicals, which have the potential to be turned into cancer drugs. Recent advances have made it possible to generate these molecules in more efficient and better ways, as well as to make these chemicals more effective against cancer cells. This publication serves to establish what is known, to inform our own efforts, funded by CIRM, to generate novel methods to target cancer stem cells.