Masechet Yevamot gets a bad rap. Many consider it amongst the most difficult masechtot to learn. Yet its seems to me it is difficult in the same sense that financial planning or preparing a tax return is difficult for many--something about numbers makes people nervous. A case of four brothers, two of whom marry two sisters and die, and one of the widows is the mother-in-law of one of the remaining brothers (Yevamot 26a) is more foreign than difficult.
These types of cases--and Yevamot has many of them--may sound scary, but with a pen and paper (something that many of our predecessors who studied this did not have), they are much easier to follow. What makes Yevamot difficult for some, it seems to me, is the fact that for us moderns its underlying concepts are no longer relevant.
Masechet Yevamot rests on two principles which are no longer applicable: polygamy and yibum itself. The mitzvah of yibum requires that, in the tragic situation of a man who dies childless, one of his brothers is to marry his widowed sister-in-law. While the Torah has an alternative if they do not want to marry, chalitzah, it is clear the preference of the Torah is for yibum. A central element of the chalitzah ceremony is the wife spitting on the ground next to the man who spurned her, declaring, "Thus should be done to the man who does not build the house of his brother" (Devarim 25:9).
For us moderns, the idea that one would marry a woman to keep the lineage of his deceased brother alive is a foreign one, to say the least. But in ancient societies, and in many that still exist today--including those Western countries that maintain a monarchy--marriage was, more times than not, a way of solidifying power, pedigree, or prestige. Most today marry based on numerous factors, starting with love and including (we hope) character, family, status, or even money. Even those who rely on their parents to choose their marriage partners are unlikely to let their brothers do so.
In a truly insightful and, dare I say, courageous move, our rabbis pretty much outlawed yibum, insisting that one always perform chalitzah instead. It is a tremendous act of kindness to marry in order to keep alive the name of one's brother, and one that most are incapable of doing. "Yibum was initially preferred, as one had intention for the mitzvah; but now that they do not intend for the mitzvah, it was said that the mitzvah of chalitzah takes precedence over the mitzvah of yibum" (Bechorot 13a).
Yibum itself could only be practical in a society where polygamy was allowed, as oftentimes, fulfilling the mitzvah of yibum meant practicing polygamy. The extent to which modern man has distanced himself from polygamy is amply demonstrated by the fact that most of the Western world has sanctioned gay marriage, but criminalizes a polygamous one.
Unlike yibum, the Torah never considered polygamy a mitzvah or even something desirable. The most famous Biblical polygamous marriage, that of Yaakov, Leah, and Rachel, did not turn out so well, with loving sisters becoming bitter rivals. "If a man has two wives, one whom he loves and one whom he hates" (Devarim 21:15) is a description of the natural course of events. Nonetheless, polygamy was allowed and in a society where death was a common occupational hazard, where many men were killed in battle (or, in the case of Jewish men, by their hostile neighbours), and death by disease was rampant, polygamy may have made much sense[1]. Once polygamy was banned by Rabbeinu Gershom in the 10th century (and for Sephardim by the State of Israel), yibum was effectively banished with it.
Yet despite the fact that yibum (and polygamy) are no longer being practiced, there is much practical material in the masechet. Of course, the mitzvah of chalitzah is still applicable and very necessary; until such is done, the women is an agunah. The first mitzvah of the Torah, pru u'revu, is explicated in our masechet, as are the details of many forbidden marriages. Perhaps most significant are the special rules regarding the much lower standard of evidence needed in order to declare a man dead and thus declare his widow eligible for remarriage.
[1] While disease and persecution may have affected women as much as men--though it is likely that men were murdered at a higher rate than women--there was much dislocation of family life, and worrying about whether a man was married was of lesser importance than remarrying itself.