4-4 point low approach one-space low pincer, tenuki
When White ignores Black's pincer here, it is most usual to play on top (marked stone). Black at a is another possibility.
White may simply take up position on the side as shown, allowing Black the good shape bulge play at . This would be part of an overall plan.
White can get enough by wedging in at to live, if Black responds on the outside at . This is joseki, with White completing the shape with 11 at a.
Black can also play from the inside with here. This is fashionable, having been played often by pros in 2002. Now Black at a involves a ladder question; but playing as shown in the diagram is forceful.
This continuation is being played currently: White has some other options, but (similar to the solid connection in the staircase) leads into a pushing battle in the centre.