Histone lysine-specific demethylase 1 (LSD1/KDM1A) has become an important and promising anticancer target since it was first identified in 2004 and specially demethylates lysine residues of histone H3K4me1/2 and H3K9me1/2. LSD1 is ubiquitously overexpressed in diverse cancers, and abrogation of LSD1 results in inhibition of proliferation, invasion, and migration in cancer cells. Over the past decade, a number of biologically active small-molecule LSD1 inhibitors have been developed. To date, six trans-2-phenylcyclopropylamine (TCP)-based LSD1 inhibitors (including TCP, ORY-1001, GSK-2879552, INCB059872, IMG-7289, and ORY-2001) that covalently bind to the flavin adenine dinucleotide (FAD) within the LSD1 catalytic cavity have already entered into clinical trials. Here, we provide an overview about the structures, activities, and structure-activity relationship (SAR) of TCP-based LSD1 inhibitors that mainly covers the literature from 2008 to date. The opportunities, challenges, and future research directions in this emerging and promising field are also discussed.