Post-translational modifications of histone play important roles in gene transcription. Aberrant methylation of histone lysine sidechains have been often found in cancer. Lysine specific demethylase 1 (LSD1), which can demethylate histone H3 lysine 4 (H3K4) and other proteins, has recently been found to be a drug target for acute myeloid leukemia. To understand structure activity/selectivity relationships of LSD1 inhibitors, several series of cyclopropylamine and related compounds were synthesized and tested for their activities against LSD1 and related monoamine oxidase (MAO) A and B. Several cyclopropylamine containing compounds were found to be highly potent and selective inhibitors of LSD1. A novel series cyclopropylimine compounds also exhibited strong inhibitory activity against LSD1. Structure activity relationships (SAR) of these compounds are discussed. Docking studies were performed to provide possible binding models of a representative compound in LSD1 and MAO-A. Moreover, these modeling studies can rationalize the observed SARs and selectivity.