  In this review we discuss hidden symmetries of toroidal compactifications of
eleven-dimensional supergravity. We recall alternative versions of this theory
which exhibit traces of the hidden symmetries when still retaining the massive
Kaluza-Klein states. We reconsider them in the broader perspective of M-theory
which incorporates a more extended variety of BPS states. We also argue for a
new geometry that may underly these theories. All our arguments point towards
an extension of the number of space-time coordinates beyond eleven.
