Enemy explained [spoilers]
For those of you struggling to understand this movie, it really is very simple and linear...
It begins with Anthony arriving late to a high level secret meeting of politicians and important people at a sex club. There is clearly a major inter-species war with the spiders about to commence and we get the impression that tensions are running high. A messenger from the spiders is brought into the meeting, presumably to deliver the demands of his master, however it is a trap and he is immediately assassinated by an undercover agent disguised as a stripper.
We cut to Adam. He is the hero of the story and is working in an undercover job at a university while he attempts to thwart a sleeper cell of shapeshifting spider spys and retrieve a stolen key, he uses his lectures to try and attempt to soften the blow of the forthcoming enslavement of the human race by spiders by trying to educate his students as to what live will be like after the war has been lost. "It is all about control!".
In the evenings he spends his time at a safe house, where he continues his research and ocassionally has sex with his girlfriend. One day at the university he is tipped off by a suspiciously helpful co-worker, who recommends a movie to him. We must assume that this is no coincidence and it is most likely that the co-worker is a shape-shifting spider that has become disillusioned with his leaders and wishes to aid the humans. We never see him again so it is likely he was executed or committed suicide shortly after.
After watching the movie, he notices that there is a man in the film who looks exactly like him. Adam realises that the spiders have cloned him, that the movie recommendation was a tip-off and that this man must be connected to the undercover cell of shape-shifting spiders. He realises that he must meet this man and that he can use the concept of doppelgängers to make Anthony, who we now know is a spider spy with access to high level meetings of politicians using the stolen key, believe his interest in him is purely innocent and based on their physical similarities.
Adam manages to pick-up instructions intended for Anthony at a designated spider intel drop-off point, disguised as an acting agency. He tries to contact Anthony but raises the suspicions of his wife who then visits him at his school to scope him out. Adam acts reasonably normal enough so that she does not suspect he is onto them, however she immediately calls Anthony and alerts him [off screen] of the issue. We also see she has an enlarged abdomen like a spider.
Adam foresees a half-morphed spider woman in his dream as he begins to realise how hard it is to tell real humans from the spiders. Anthony contacts Adam and arranges to meet him at a secluded location, using his special powers he evaluates Adam and corners him - however, Adam senses danger and escapes leading to a motorway chase. Anthony catches Adam but, unable to morph into a spider while on a motorcycle without drawing attention, he lets Adam escape.
The huge master of spiders is briefly seen stalking Toronto, it is to be assumed that it has released some form of noxious gas at this point to paralyze the inhabitants of the city so that they are unaware of his presence. It is clear though that the final end game approaches and Adam must act fast.
Anthony returns to visit Adam, having formulated a plan to kidnap his girlfriend. He pulls off the plan and leaves with the girlfriend, promising to return her the next day and leave Adam alone - it is clear at this point that Anthony knows Adam knows he is a spider and is taking his girlfriend hostage as a bargaining chip. Anthony takes the girlfriend, but while fighting with her in a hotel room she realises that something is not right and demands to be freed.
Meanwhile, Adam goes to Anthony and his wife's lair and snoops around looking for clues. When Anthony's wife returns home she immediately senses that something is not right with 'Anthony' but is forced to play it cool and act normal so as not to blow her cover. Anthony is now seen driving with urgency with the girlfriend, taking her to a final lair where she will be executed and digested by the master spider. Fortunately, she manages to overpower him and kill Anthony in the most heroic manner - killing herself in the process.
Adam and Anthony's wife continue their mind games back at the apartment. She has sex with him, a known prelude to murder in the spider community, but before she can kill him he discovers the stolen key - he had had it all along in the spider intel package. With his mission complete he heads to the bedroom to execute the wife, realising the game is up she reverts to her true form and cowers in fear as Adam smiles at having outsmarted the spiders.