How does "challenging" work? On close line calls, sometimes there is a graphic showing whether the shuttle was in or out, but other times players just discuss with the umpire, and the match goes on. What's happening in these cases?
At high-level tournaments (sometimes only on TV courts), the HawkEye Instant Review System (IRS, informally challenging) allows players - or if neither line judge nor umpire could see the shuttle, the umpire - to challenge line judges' and umpires' decisions. It is regulated by section 4.1.8 of the laws.
As long as the challenges are successful in overturning the line judge's decision, players can challenge as often as they want. To prevent abuse, each side is limited to two unsuccessful challenges per game (until 2015 per match). Players must challenge immediately after the decision, and must not consult with coaches - so when you see an umpire denying a challenge, the player took to long to decide whether to challenge. Typically, players will raise one finger to indicate that they are challenging.
The umpire will then raise their left arm to indicate to the referee that a challenge has been made. The HawkEye system, aided by a technician, will then make a decision. Previously, an off-court umpire (on IRS duty) would review the footage and make the decision. In any case, the decision gets relayed to the umpire, and a corresponding video shown to the audience.
In case of an unsuccessful challenge, the umpire will announce the (unchanged) score and how many challenges are remaining. In case of a successful challenge, the umpire will announce the corrected score.
If the line judge and umpire were not able to make a determination In or Out (e.g. because a player was between line judge and shuttle), the umpire can also call IRS themselves.
IRS is not available on every line; the service lines are not covered by current implementations due to cost reasons.
Only line calls can be challenged. Any fault or let calls are final. In the future, a similar system may be available for service fault calls, and may be fully automated so that a decision can be made immediately, whereupon the procedures laid out above are likely to change.