Hard sudoku
This is where you start holding more than one fact in mind at once. Hard puzzles typically need a naked pair or hidden pair — two cells that, between them, can only hold two particular digits — plus the row/column-first mirror of locked candidates, claiming. Occasionally a puzzle at this level needs a naked triple, the three-cell version of the same idea, though that shows up less often than pairs do.
None of this is guessing. A naked pair in r2c3 and r2c8, both narrowed down to just "4 or 7," tells you with certainty that no other cell in row 2 can be a 4 or a 7 — even though you don't yet know which of the two cells is which. That's the shift from easy and medium: you're tracking relationships between cells, not just reading off a single forced answer.
Who hard suits
You've played enough sudoku that singles feel automatic and you want the board to actually push back. This level rewards methodical notes — if you're not pencilling in candidates yet, this is the point where it stops being optional.
A note on pacing
It's normal to stall for a while here. Scan every row, column, and box specifically for cells with exactly two or three candidates left — pairs and triples hide in plain sight once you're looking for the right shape instead of the right digit.
When pairs and triples start feeling routine, expert introduces a pattern that spans two entire rows or columns at once.