Stealth

With Update 7.0, new mechanics for stealth offer a better and easier time doing full stealth runs. This is only the first update on the likes, so expect tweaks in the near future.

How to prompt an assassination
When the crew haven't been alerted to your presence, you are elegible for performing stealth attacks. In order to do so, approach an enemy from behind (crouching for best effect), without alerting anyone to your presense, and press 'E' when the prompt appears. Depending on what frame you are using and which weapon, different animations will occur. Successfully pulling off a stealth attack will deal damage with a large multiplier (most likely different for weapon types, ie. short, long and heavy).

Detection
Here is what is known to me for now (please add to this) Grineer are the most basic and least varied in design, and all Grineer can be assassinated (or at least attempt to do so) so the following mostly refers to Grineer behaviour.
 * Crouch for better sneak runs. You'll have a smaller model so you can hide your silhouette better. This is harder for larger frames like Rhino and Frost. The speed you have while crouching is also a good amount for timing your melee, so that you dont bump into the target by accident or melee before the prompt appears
 * Noise caused by your weapons or abilities will alert enemies (shooting, meleeing the environment, Decoy, etc.). Sounds like breaking fans or storage containers or opening doors will NOT attract attention (even though they are so god damn loud (and the debris!!)). Certain weapons make less noise (Paris, and only Paris so far, I think), thus are less likely to attract attention.
 * Their range of view is <180 degrees, so crouching still in a corner is a legitimate way to expose the back of a Grineer that just walked through a door. It also is bad at detecting things at a distance (pretty short distance too) and anything somewhat above them. Move too quickly or stop crouching, and you might be detected. If you bump into them, they'll grunt and be alerted of your presense (NEEDS TEST: result of bumping into somebody while invisible). Hiding behind terrain will conceal your presense.
 * Performing the stealth attack and not killing the enemy will cause alarm (happens alot when in a high level area, or on heavy grineers with shields)
 * If you are ever forced to reveal yourself to something (camera, failed to kill, missed, etc.) you can still remain undetected if you kill/destroy everything before a console is touched, and before others in other rooms are alerted.
 * Cameras make loud alarms when they see you, but again, if they are destroyed and nothing is in range to take advantage of their alert, you're safe. Rooms with 2 cameras are very hard to get past without spending energy or alerting people.

Holes in the mechanics
Since the concept of stealth is still a new one, there are some gripes that have not been addressed.
 * The practicality of attempting assassination on durable opponents (Shielded heavy Grineer, etc.)
 * Unable to attempt assassination on Moas, Ospreys, Ancients, Canines (or its just really hard to prompt), Cameras, and Bosses. This makes the stealth approach a bad one against Corpus and Infected.
 * After each stealth attack, you finish standing up, which might reveal your position. Its also a tedious extra button press to resume stealthy activity.