In Practice it has been observed that Queen vs Rook endgame is difficult though it was believed to be quite easy to force win.
Muller in his book 'Fundamental Chess Endings'
"The Appearance of Computer databases in 1978 caused the ending to be seen in new light.While they confirmed that the queen should win from all normal starting positions, they also showed that it was quite difficult to win if the defender played precisely."
In the first part, we will see fortress position where defender gets draw by force with the help of perpetual checks and stalemate tricks.
As you can see in the diagram, with black to move ; draw can be achieved by
2. Kf5 Rf7+
3. Kg6 Rg7+
4. Kf6 Perpetual checks (4. Kh6 Rh7+ 5. Kxh7 Stalemate trick works)
4... Rg6+ Again Stalemate tricks works well for defender
1/2 - 1/2
In part 2 we will see winning method for stronger side.