An entire tractate of the Mishnah, Yevamot, is devoted to the law, and its length is a measure of how complicated the institution becomes once other rules apply to it. The tractate works through cases in which the surviving brother is already married to a relative of the widow, in which there are several brothers, in which a brother is a minor, and in which the marriage would be forbidden on other grounds, and it is one of the hardest tractates in the Talmud.
The tradition then moved from preferring the marriage to preferring the release. The argument turned on motive: the law contemplates a man acting to raise up a name for his brother, and the rabbis increasingly doubted that a man in a later generation would be acting for that reason rather than for his own. Abba Shaul is cited early for the position that a levirate marriage entered for any other motive is close to a forbidden union. Medieval authorities divided, with Ashkenazi practice moving decisively towards chalitzah, in part because the ban on plural marriage made the case impossible where the brother was already married, and Sephardi practice retaining the marriage as the preferred option longer.
The Israeli rabbinate settled the matter for the modern state in the middle of the twentieth century by requiring the release, so a widow in that position obtains chalitzah and is then free to remarry. Obligations on a brother or kinsman to marry a widow are attested in many other societies, and those are independent institutions rather than descendants of this law.