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.

It depends whether it's an active crack...you could repair it only to have it reappear in future months as it settles some more. If it's not active land it's really a hairline you could just mix some mortar to a fairly thin consistency and and use a trowel to force it into the crack. You should be aware that the new material will typically show up as lighter and make the crack more noticeable. You could also go to a mason's supply store and get something like one of the Ardex Engineered Cement products specifically for such repairs. You might want to look at the Ardex site as it has a lot of info on its products and how to use them for repairs. Here is a link that might be useful: Ardex

porcelain would be slippery we'd recommend Advantage Deck Tiles they are made from woods more durable than teak and do not require the maintenance of traditional wood. They snap together over old concrete and there is a pedestal system too.

Previously the area had a small concrete pad that had a deck built over the pad. The Deck was sagging when we bought the home and we found that the deck supports sitting on the very end of the original pad had cracked it. The base from the original concrete pad was used and expanded upon which was made up of mainly sand it appeared. It was compacted and poured at 4" allowing proper time to cure and dry. Soil in our area is a lot of clay but the the top soil that is used with grading is a large amount of sand. The general contractor we used is a friend and does not seemed concerned with anything his concrete team did or didn't due and said it is most likely happening now because after the very wet May/June we had, it is now getting really dry and will most likely move back once it is wet again.