This Colloquium reviews the studies of exotic type of low-energy nuclear fission, the beta-delayed fission (bDF). Emphasis is made on the new data from very neutron-deficient nuclei in the lead region, previously scarcely studied as far as fission is concerned. These data establish the new region of asymmetric fission in addition to the previously known one in the transuranium nuclei. New production and identification techniques, which emerged in the last two decades, such as the wider use of electromagnetic separators and the application of selective laser ionization to produce intense isotopically or even isomerically pure radioactive beams are highlighted. A critical analysis of presently available DF data is presented and the importance of detailed quantitative DF studies, which become possible now, is stressed, along with the recent theory efforts in the domain of low-energy fission.