The Compromise of 1850 was pretty much a direct result of the Missouri Compromise. The split down the middle of the country mandated by the Missouri Compromise was immediately recognized as a potentially devastating move by anyone with any political foresight whatsoever. Henry Clay and his pals simply thought they'd just patch together another compromise should that prove necessary, which it did in 1850 (of course).
Did this finally address the issue of slavery?
In yet another stunning episode of apathy towards the plight of slaves, Clay and co. decided that another "don't rock the boat" approach was just the thing the country needed to see it through this whole slavery mess. This turned out to be an incredibly massive mistake, but thankfully for the main forces behind the compromise, they'd all be dead by the time it came to bite America in the butt.
What's this? An actual attempt to resolve the issue of slavery in America? That's right. We know, we're shocked as well.
It took the largest war in U.S. history to get it done, but good ol' Honest Abe finally managed to do something about the whole "people as property" thing that had eating at America for the past century and more.
Of course, this didn't really end the systemic plight of Black Americans, but at least they weren't legally property, even if their situation was basically the same.
The act that would come to supersede the Missouri Compromise right before it ceased to matter at all. Passed in 1854, the Kansas Nebraska Act was initially intended to address the issue of the many miles of open farmland available in the western United States.
A clause of the Act addressed the issue of slavery democratically: state constitutions would be drafted based on popular sovereignty, such that the majority would decide which way a given state would lean.
This is a striking example of why democracy might not be such a good thing, as this clause resulted in the famed Bleeding Kansas incident, in which settlers flooded into Kansas in order to gain a majority for their faction of choice.
A failed compromise proposed on the eve of the Civil War by Senator John J. Crittenden. The goal of the compromise was to prevent civil war and bring an end to the slavery issue once and for all.
It was designed to contain slavery to states in which it was currently allowed, and that any new territories or states would be forbidden from engaging in slavery.
This half-measure satisfied neither abolitionists nor slavers (surprise, surprise) and so the last chance at avoiding the Civil War was left by the wayside.
The final nail in the Missouri Compromise's coffin, this Supreme Court Case struck down the Compromise as unconstitutional based on the grounds that any "n****, whose ancestors were imported into [the U.S.], and sold as slaves" was not a citizen and therefore not subject to U.S. Federal law. (Source)
Also, the Supreme Court found that the Federal government had no say in the matter of slavery for any state or territory added after the formation of the United States in the late 18th century. The Supreme Court Chief Justice Roger B. Taney believed this would set the matter of slavery to rest…but it only raised the stakes and make abolitionist parties in the North boiling mad.