Pros are they can take very high temperatures, you can be rough with them, are non-stick when seasoned and at a proper temperature (like cast iron), and much lighter than cast iron.
Cons are you don't want to cook liquidy acidic foods in them that often (removes the seasoning off the pan), they can rust easily if not seasoned, and require slightly more maintenance then stainless steel or Teflon pans. Basically you're not washing these with dish soap. Just a rinse, maybe some scrubbing with kosher salt, and heating it on the stove to dry and sterilize it.
Keeping it lightly oiled when cooking or storing it helps too. They're a great work-horse pans. We got ours after having to throw out our last scratched Teflon pans. Making scrambled eggs in carbon steel was hard at first, but over time as a better seasoning developed and figuring out the right temperatures to use, I now get the same results as I use to in Teflon.
By complete accident my spatula is also from DeBuyer (https://www.debuyer.com/en/flexible-turner-slotted-fkofficiu...). It is very sharp and it easily scrapes anything that dares to stick (due to my mistake of not getting it hot enough), without smearing it.