Using Field Calculator in QGIS to update columns with centroid coordinates

Not sure if it worked 5 years ago, but now the solution looks like this:

x(centroid($geometry))

and

y(centroid($geometry))

Results are the same as while using the "Join" option mentioned above:

A fast way (without field calculator) would be to

1. create a centroid layer: Vector - Geometry Tools - Polygon Centroids
2. join the centroid layer to the polygon layer: (Polygon) Layer Properties - Join tab