I have one that looks very similar running the full width of my driveway. I asked the concrete company about a repair, but only got a lot of reasons to leave it be. They said a patch would look worse than the crack. They said removing and replacing the cracked section between the expansion joints would disturb the substrate and lead to more cracking. Basically, they told me to wait and see if it separated further. In that case, they would treat it with an epoxy injection. So we're living with it and waiting, mostly because we weren't offered any other alternative. Hope you have better luck with yours. Totally Confused

This is a very common issue that arises when concrete stoops are built separately from the house, typically with no compaction of the underlying soil. For decades now, new home builders have avoided the problem by just delivering the home with a couple of pre-cast steps that many homeowners replace with more elaborate landscaped steps. In short: there is no permanent cure. You can remove them altogether, then either: excavate to undisturbed soil below the frostline and lay a proper footing and foundation and poured steps, tied into the existing foundation; or prepare a compacted base and have one-piece pre-cast porch or multi-piece pre-cast steps installed, as in the pic below. Everything else is a cosmetic stopgap. If replacing the existing threshold is on your list, you might want to see if an additional one could be extended over the intersection between the sinking stoop and the house.

We hired a contractor to reface our entire concrete porch, including the flush brick trim and steps, in Pennsylavania Gray Flagstone. Assuming you don't want to do anything that drastic---you might be able to use concrete patch on the crack then repaint as brickeyee suggested. There are specific paint formulas just for concrete.

That your existing concrete is in good shape is key. Any crack in it would transfer through to the new material. So long as you create proper finish levels, you should be in good shape. Stamped concrete can look terrific. It's biggest drawback is the color not being integral to the slab, but just surface treatment. This is really no problem unless it is subject to harsh wear, which in this instance is probably not going to be the case. If the surface gets a chip or gouge, you'll see near-white concrete below. In most residential situations, it doesn't get that harsh of treatment.