New strategies using biological agents are being developed to treat cancer. Live viruses are among these new agents. Virotherapy uses replication-competent viral vectors with strong oncolytic properties. With the use of molecular virology techniques, viruses have been genetically engineered to replicate selectively in tumour cells and are under preclinical and clinical investigation at present. Measles virus (MV) is being used for this purpose. Replication-competent attenuated Edmonston B measles vaccine strain (MV-Edm) is non-pathogenic and has potent antitumour activity against several human tumours. The virus is selectively oncolytic in tumour cells, eliciting extensive cell-to-cell fusion and ultimately leading to cell death. Therefore, MV-Edm is a safe and efficient means to kill tumour cells. Further improvements in existing MV vectors may increase tumour selectivity and oncolytic activity. This review discusses the discovery and development of replication-competent oncolytic MV for cancer therapy.