The talk proceeds as follows: (1) we summarize OT and its applications to UG. The we present (2) learning and (3) parsing algorithms for OT. Finally, (4) we show how crucial elements of OT emerge from connectionism, and discuss the one central feature of OT which so far eludes connectionist explanation. (1) In OT, UG provides a set of highly general universal constraints which apply in parallel to assess the wellformedness of possible structural descriptions of linguistic inputs.