For those convicted of felonies, this generally comes with the stipulation that they cannot buy or possess firearms. While there are some exceptions, the general rule of thumb is that gun rights are lost to those with a felony record.
On the other hand, those with a misdemeanor are often allowed to purchase firearms. However, these laws have been changing rapidly in recent years, and it's important to keep up with the changes. You certainly don't want to do anything that gets you into legal trouble just because you assumed that the law was the same as it has been in the past.
States set their own gun laws, and Colorado decided to update theirs after a mass shooting last year. They did this with House Bill 1298. The gunman who was involved in that shooting had already been arrested for third-degree assault and convicted. This is a misdemeanor, but he was still allowed to possess a firearm. Third-degree assault is now one of a number of different misdemeanor convictions that can take away gun rights in the state.
Interestingly, though, the bill also made it so that some felonies that previously eliminated gun rights now no longer do so. For instance, some individuals who were convicted on drug offenses may now be allowed to have a gun when they couldn't have one before. The same is true for some with theft convictions or charges for criminal impersonation.
This is certainly not an exhaustive list of all the changes, but it shows you how gun laws are not static and they can change with the events and the times. It's important to know how these changes have occurred and how they may impact your case if you are already facing charges of your own.