The EMP grenade can either be thrown or mounted on walls. When it explodes, the grenade will disable any robots. If the player is the blast radius, it will drain their bioelectricity. If the EMP is mounted on a wall, it will detonate when anything gets near it.
Technically, what the EMP grenade does is drain a target's EMP health. Robots and other mechanical devices have EMP health, but purely organic foes, like National Secessionist Forces terrorists, do not.
EMP Grenades are formally introduced by Anna Navarre at Battery Park after the player locates the Ambrosia container. Depending on the response, the player will receive either one or two grenades (Anna dislikes the "nerves of steel" comment).
A good way to avoid danger is to peek into a new area by leaning. If there are any robots in the area, take out an EMP and either make it bounce over a wall so that enters the new area without the player having to be there, or quickly run in and toss the grenade, then head to cover. This will ensure that the robot will be disabled without the player taking any damage.
Sneaky players can plant an EMP grenade on a wall in the robot's patrol route so that, when the robot is walking around, it will set off the EMP, disabling it (or in the the case of the larger robots, doing a lot of EMP damage). Areas like the outside part of the Cathedrale de Payens are a good place to use this. Larger robots will likely need two EMPs next to each other in order for it to be disabled.
Players with explosive weapons can use EMP grenades to conserve ammo for their explosive weapons. Instead of using a GEP gun to take down a robot, they can use an EMP to take it down, saving the rocket for something like a door they may need to blow up later. This is particularly useful for those that have a little bit of explosive ammo and need to conserve it.
EMPs can also be used to quickly take down security cameras or tripwires if they can't access a panel or a fuze box to shut them down. Simply lob the grenade near the device and wait for the grenade to explode. Once it blows up, the device will be down and the player can slip by without triggering an alarm.
Like other grenades, the EMP grenade can be used to climb up walls.