First two centres
Planned in inspection.
The Yau method
Named after Robert Yau, who made it popular, Yau is the standard 4x4 method among fast solvers: two opposite centres (usually the cross colour and its opposite), three cross dedges paired and placed around the bottom centre, the last four centres, the last cross dedge, then the remaining edges, and the 3x3 stage. Solving three cross dedges early, while there is still room to move edges freely, means the cross is already done when the 3x3 stage starts, and the last centres are built in the space the cross leaves.