Depending on which jurisdiction you live in, covering an outdoor kitchen can be a code violation.
You have to dig deeper though, what does it mean to “cover” an outdoor kitchen? In many cases, people are intending to put a solid roof over it to keep out of the elements. In the Carolina’s, there are many counties that will only allow this if you purchase and install a hood vent to take the fumes through the roof of the structure. These can be quite costly and you really need an expert to install it properly
In some counties, if the roof is not screened in and you put the cooking station on the perimeter of the roof, they allow that to pass.
A common cover is a pergola like the one featured above left. This is allowed in all jurisdictions because the covering is not solid allowing the fumes to dissipate. Pergolas are very appealing aesthetically and do provide some protection from the sun if there are enough timbers installed above. They do not however keep the rain from hitting you.
Retractable awnings are another form of cover and there are no building codes against awnings. Make sure you check with a licensed general contractor or the county building department to see what your options are. If you want to see a complete photo gallery of outdoor kitchens, go to archadeckofcharlotte.com