  In this talk I report on the results of a complete O(\alpha) calculation of
leptonic \mu-decay. The calculation is complete in the sense that all
polarization and mass effects have been included in the radiative corrections.
I mostly concentrate on the longitudinal polarization of the electron which
considerably differs from the naive value P_e^l=-1 in the threshold region,
both for the Born term and more so for the radiatively corrected case. I also
discuss the role of the O(\alpha) anomalous spin-flip contribution and its
description in terms of the equivalent particle approach which survives the m_e
-> 0 limit. Finally, I provide a brief account of the history of the O(\alpha)
radiative corrections to leptonic \mu-decay. I trace the error done in the
first (wrong) 1956 calculation of Behrends, Finkelstein and Sirlin. My account
of this historical error differs from that recently given in a talk by
Kinoshita on the occasion of the 70th birthday of Sirlin.
