When is a rally replayed as a let?

Under Law 14 of the BWF Laws of Badminton, a "let" is called by the umpire, or by a player if there's no umpire. It's a let if:

• the server serves before the receiver is ready (but if the receiver tries to return it, they're treated as ready);
• during the serve, the server and receiver are both at fault;
• after the serve has been returned, the shuttle is caught on the net and stays on top, or passes over and is caught in the net (in wheelchair badminton these are faults instead);
• the shuttle disintegrates in play and the base completely separates from the rest;
• in the umpire's opinion, a coach disrupts play or distracts a player of the opposing side;
• a line judge is unsighted and the umpire can't decide; or
• any unforeseen or accidental situation occurs.

On a let, play since the last serve doesn't count, and the player who served last serves again.

Note the difference on the serve: a serve that's caught on top of the net, or caught in the net after crossing it, is a fault, not a let.