What most people don't know (but I learned from Jay Winik's excellent book, April 1865: The Month That Saved America) is that the military and political leadership of both the Union and the Confederacy were involved in momentous decisions in April that helped bring the war to an end, and bring the country back together. These were decisions that, had they been made differently, could've resulted in catastrophe for our nation. Even if the Union had won the war, and the South readmitted, our identity as a unified country might have been in jeopardy had these decisions been made differently.
As Winik points out, using contemporary examples, some countries and regions never fully recover from civil wars. To increase the probability of long-lasting peace, Lincoln and Grant chose to disregard the railings of those who would bring shame and severe punishment on the heads of their conquered enemy. Though Jefferson Davis was all for a last-ditch attempt at preserving the Confederacy by sending the army into the hills for prolonged guerrilla warfare, Lee chose the high road, knowing the impact of a sustained war would only make matters far worse than they already were. Winik covers both the strengths and faults of Lincoln, Grant, Lee, Sherman, Johnson, Davis, and Forrest, and shows that, despite these faults, they made the decisions at the end of the war that enabled the U.S. to come back together.
The only thing I wish Winik had not omitted was a discussion of Lincoln's presidential pardons for high-ranking Confederate officers and officials, and how that played out with Andrew Johnson once he assumed the presidency. I believe Lincoln's policies in this regard played an important role in achieving peace, and Johnson's policies almost aborted this.
For a different but equally engaging account of events in April and May 1865, I highly recommend James L. Swanson's Bloody Crimes: The Chase for Jefferson Davis and the Death Pageant for Lincoln's Corpse.