Some concrete core drilling, meaning drilling circular holes into concrete usually to run wires, conduit, or new plumbing pipes through the material, might be easy enough on your own. However, like most home improvement jobs, you don't want to assume that you can take on more than you can reasonably handle, as this is a surefire way to cause damage to your home and even injure yourself. Note a few things that can help you determine if you should tackle your own concrete core drilling or call a professional.
1. Are you sure it's really concrete, and its mixture?
When drilling through a material, you always need to know something about its overall composition. Hardwood might be more prone to crack when cut or drilled than a soft wood, as an example, so you would use different saw blades and techniques for different woods. Concrete is the same; it may all look alike to you, but some concrete is softer because of having more sand added and needing to be more pliable, but some concrete is very thick and very dense. You need to know the different drill bits and techniques to cut through each type of concrete without chipping or otherwise damaging it.
It's also good to note that you may not even been looking to cut through concrete at all. Masonry bricks, mortar, and other such materials may look like concrete, but they're made with entirely different materials and mixtures of materials. If you don't use the right drill bit for a different material, you might also cause damage.
2. Removing the drilled part
Drilling through concrete typically doesn't mean putting in a drill bit and having the cut concrete automatically feed itself out of the hole being created, the way wood chips curl up and get displaced when you drill through wood. Instead, you are usually cutting out a large, rounded portion of concrete that you need to remove in one piece. If you don't know how to actually detach the drilled part of the concrete from the remaining slab, you could easily crack the concrete in the slab.
The tools used will usually have an anchor that helps to hold the drilled part as it's removed, but if you're not familiar with how to properly set these anchors and work with removed concrete, you could easily damage the tool itself as well. A professional will know how to do this even if the drilled part is very large and very heavy.