Hard Sudoku

Singles alone will stall. These puzzles need you to clear candidates with locked candidates or naked pairs before the next digit appears.

Why notes matter now

At this level you will reach points where no single is visible. The way forward is to write candidates in each open square (use Notes) and then remove the ones that logic rules out. Two techniques do most of the work:

Locked candidates: if, inside a box, a digit can only sit in one row, it cannot sit anywhere else in that row outside the box. The same works for columns, and the other way round.
Naked pairs: two squares in the same row, column or box that can only be the same two digits. Those two digits are used up, so remove them from every other square in that unit.

Hard puzzles here start with 26 digits and are graded so these techniques, plus singles, are enough.

A routine for hard puzzles

Place every single you can find.
Fill in candidates for the remaining squares.
Look for pairs and locked candidates; remove what they rule out.
Go back to step 1. New singles almost always appear.

When hard stops being hard, try expert sudoku.