I have some knowledge of Jewish law, but it seems ambiguous to me in some areas, either because there are differing opinions, or no one has really explained to me the reasons for the opinions to be favored over the opposing opinions.
We read in Deuteronomy 24, that a ספר כריתת must be given to a wife after a divorce. This implies, of course, that the couple is married. In fact, there is sufficient Rabbinical opinion that an unmarried female companion is a Pilegesh, or concubine, which is a separate legal status.
However, in the Mishnah (Kiddushin) it is specified right at the beginning that a wife may be acquired through money, a contract or sexual intercourse. Kiddushin seems to occur when the woman accepts the sexual intercourse and participates in it.
http://www.mechon-mamre.org/jewfaq/marriage.htm
Now, it's true that rabbis today do not consider sexual intercourse a valid way of acquiring a wife, but I'm not sure what gives them the authority to take away something that is written in the Talmud.
If I have relations with my girlfriends, and then we break up, should I be giving them a bill of divorcement? If we're not risking that her future relationships will be adulterous, it's only because of rabbinical pronouncements. Obviously Orthodox rabbis today aren't too concerned with non-virgins marrying their husbands, and don't inquire too much about the get from all their sexual partners. But I am not sure how all this came about.