Pairs work inside a single unit. These two techniques work across the overlap between a box and a line — and they're what carries you through Hard puzzles once singles and pairs have both run out.
Every 3×3 box shares three cells with each of three rows, and three cells with each of three columns. That shared strip is where both techniques live. The reasoning is the same in both directions: if a digit is confined to the overlap from one side, it's confined to the overlap from the other side too, and everything outside the overlap can be cleared.
Look inside a box. If a digit's candidates in that box all fall within a single row, then the box's copy of that digit is definitely in that row. The box has to contain the digit somewhere, and every "somewhere" available is on that line.
That row already has its one and only copy accounted for inside the box — so the digit can be struck from the rest of the row, in the two neighbouring boxes.
In the diagram, 3 appears twice in the box and both instances sit in the top row of it. One of them is the real 3. Either way the row's 3 is inside this box, so the two cells further along the row lose their 3s. Three candidates in a box, all in one line, works identically — a pointing triple.
The same applies to columns. If a box's candidates for a digit all fall in one column, clear that digit from the rest of the column.
Now run it the other way. Look along a row. If a digit's candidates in that row all fall inside a single box, then the row's copy of that digit is somewhere in that box — and so the box's copy is somewhere in that row. Every other cell in the box loses the digit.
Above, the row can only place its 7 in two cells, and both belong to the same box. The box's 7 is therefore committed to that row, and the box's other six cells give up their 7s. This is sometimes called claiming, because the line claims the digit from the box.
Pointing: confined within a box → clear the rest of the line.
Box/line: confined within a line → clear the rest of the box.
Ask where you looked first. If you were scanning a box, any elimination you find lands on a line. If you were scanning a row or column, it lands in a box.
These are more mechanical to hunt than pairs, which makes them a good fallback when you're stuck and can't see anything:
Most Hard puzzles on this site are generated so that they require at least one of these two techniques. Singles and pairs alone will take you a long way and then leave you looking at a grid where every remaining cell has three or four candidates and nothing resolves. That's the signature of a locked-candidate step waiting to be found.
Once you have one elimination, the grid usually opens: a cleared candidate produces a hidden single, which produces a placement, which produces another. Expert puzzles may need X-Wing or Swordfish on top.