Reissig studied chemistry at Ludwig-Maximilians-Universität München (Germany) from 1970 to 1975, where he completed his Doctor of Philosophy in 1978 under the supervision of Rolf Huisgen, with a thesis "eue Beiträge zu den Additionen der Diazoalkane und zur Chemie der 3H-Pyrazole" (Contributions to the Additions of Diazoalkanes and the Chemistry of 3H-Pyrazoles).
After a postdoctoral research stay at University of British Columbia, Vancouver, with Edward Piers (1938–2010), he started his independent research at the Julius-Maximilians-Universität Würzburg (Germany) in 1979 under the mentorship of Siegfried Hünig finishing his habilitation in 1984 (Chemistry of Donor-Acceptor Cyclopropanes). As Heisenberg awardee and lecturer he stayed in Würzburg until 1986. From 1986 to 1993, he was associate professor at TH Darmstadt and after the German reunification full professor at Technology Union Dresden from 1993 to 1999.
Since 1999 he has been professor at Freie Universität Berlin from 1999 till his retirement in 2015.
Married Elke Seidel.