Hidden symmetries, central charges and all that

In this review we discuss hidden symmetries of toroidal compactifications o f 11-dimensional supergravity. We recall alternative versions of this theor y which exhibit traces of the hidden symmetries while still retaining the m assive Kaluza-Klein states. We reconsider them in the broader perspective o f M-theory which incorporates a more extended variety of BPS states. We als o argue for a new geometry that may underly these theories. All our argumen ts point towards an extension of the number of spacetime coordinates beyond 11.