Relationship with Gordon Freeman
Though Alyx was only a child when Freeman was employed at Black Mesa, Freeman's stasis between the events of Half-Life and Half-Life 2 has effectively erased any appreciable age gap between the two characters. Thus, sexual tension begins to arise between Alyx and Freeman during the course of their travels together. It is first witnessed during the chapter Black Mesa East, when her father tells her, "There is nothing Gordon can't handle?with the possible exception of you". She replies by embarrassedly muttering "Dad, please..."
Continuing this theme, Episode One contains many situations where this relationship is developed. Alyx hugs Gordon when her robot, Dog, finds him, and at one point she jokingly asks him if there is room for two in his HEV suit. Barney Calhoun additionally mentions that Freeman is a "lucky dog" to travel alongside Alyx.
In Episode Two, when the characters reach the White Forest facility, Eli mentions that, with the reproductive suppression field turned off, Alyx and Gordon should "do their part" for the revival of the species, to which Alyx responds with an embarrassed chuckle. He replies that she can't blame him for wanting grandchildren. During the middle segment of the game, when Gordon and Alyx drive across country in a modified vehicle, Alyx can be seen winking at Freeman. Finally, and perhaps most notably, the Vortigaunts "Weave the Freeman's life with hers," while reviving and healing Alyx, thus explicitly connecting the respective well-being of the two characters.
The game commentary that is given during the "elevator scene," in which Gordon waits for the elevator that takes him down to the core, verifies that such a relationship was intended.