There are two main issues that remain from the Civil War period.
First, there is the basic political issue that caused the Civil War. This is the issue of states’ rights and federalism. The issue is nowhere near as salient today as it was at the time of the Civil War, but it does still remain with us. Many conservatives believe that the states need to be given back more of the powers they once had. They believe that the federal government has become too strong. This is part, for example, of the reason why Republicans are so deeply opposed to “Obamacare.”
Second, there is the issue of African American rights. Of course, we are no longer fighting over slavery, but there are still issues about the rights of African Americans. We still argue about what, if anything, needs to be done to make up for the disadvantages that have come to African Americans because their ancestors were enslaved and then discriminated against. This is an issue that is closely related to, though not exactly the same as, the issue of slavery that was so important at the time of the Civil War.