I did research on facial attractiveness for years at a major university and published in the field. AMA
Update 7 PM GMT on April 23: Thanks for all of the interest & the questions (and the Gold). The conversation really went in a lot of directions & it was interesting to see it unfold.
I did most of this AMA in 20 hrs straight (like a lunatic) - so my wording was not always the best & there might be some unclear statements. I've tried to make some edits to clear things up more. In general, this topic is more complex than it might seem on the surface. We have many different kinds of preferences and even 100 studies measuring those preferences just scratches the surface. Also, there are rarely black & white answers in this field, though we can usually spot trends. Even since the AMA, I've argued about some of the questions with people I know who have done similar research. Plastic surgeons have huge disagreements over techniques and what is aesthetically pleasing too. So, all of this has to be taken in that context. There are no absolutes in this area because of subjectivity - though we can understand a great deal about the topic based on things that are repeatable in research studies (and thus, more likely to be objective).
TL;dr: Facial attractiveness has a lot of components like symmetry, sexual dimorphism, skin quality, facial ratios, "averageness" (how much your features represent the average in the population - like the average length nose), and a viewer's personal preference (which can make up a large % of the equation). So, it's complicated & sometimes contradictory, as research often can be. There are still a lot more questions than answers in the field. At least we know some of the major components - and this info is based on empirical research in psychology, literature from plastic surgeons, and a little bit of literature from art.