picozeta

The method described here nowadays goes under the name of CFOP (Fridrich's page made it very popular, so in former days it was referred to the "Fridrich" method). It's still popular and got refined over the years, see this excellent comment in this thread: https://news.ycombinator.com/item?id=37430854

Another interesting topic is the question which (cross) color you choose: There are 6 possibilities (colors) and in the beginning even top solvers preferred one color (white is the most popular) to simplify recognition ("where are my pieces?").

Later, top solvers switched to "color neutral" solving, which in theory gives you more efficient crosses, as you can choose the color that gives you the shortest solution. There even seemed to be consensus that if you want to be at the top you had to be color neutral.

However even more recently this has been challenged and "dual color neutral" (only choosing between white and yellow) seems to be the way to go.

The reason is that during inspection (in competition you have 15 seconds to "inspect" the cube meaning to plan your solution (partly) ahead of time) the selection process to choose the best cross obviously takes some time. There's a trade-off between investing time to plan the cross (and additional blocks) in inspection and selecting the color that should be preferred.