It was Mark Davies who started the cyclic revolution, with a peal of Brave New World Bob Royal in 1998. I became interested in cyclic methods in April 2002, and with some help from Richard Smith, found and pealed the right-place plain major methods Anglia Cyclic Bob and Purple Cyclic Bob a couple of months later. All of these methods have rotational symmetry; it is not possible to have conventional (palindromic) symmetry with cyclic leadheads.
Two big breakthroughs happened in 2002. The first came when I thought of using 'glide' symmetry for cyclic methods. This allowed pitch-increasing runs, and greater elegance in the line. This resulted in peals of Resurrection Cyclic Bob Royal, and Double Cambridge Cyclic Bob Major. The second breakthrough happened when Mark Davies picked up on a comment from Philip Saddleton on the ringing-chat mailing list, and produced a cyclic method with 'offset symmetry'. This works best on ten bells.
Tony Smith has recently pulished a collection of horizontally-reflective Plain and Treble Dodging Major methods with cyclic half lead heads and cyclic lead heads and rotational-symmetric methods with cyclic half lead ends and cyclic lead heads. The methods are limited to those produced by triple and quadruple changes with no more than two consecutive blows in the same position and which do not have the penultimate place made outside of the half-lead. The collection can be found on the CC methods committee website.