There seem to be two schools of thought for outdoor kitchens: they should either supplement the indoor kitchen, or they should duplicate it.
In the supplement option, the kitchen moves smoky or messy functions outside. This obviously applies to grills and barbecues, but can also work with wok rings, wood fired ovens, and other equipment that can generate smoke or spattering oil. They don’t need sinks, refrigerators, or other features that are already present in the house, although these can be present.
For the duplicate option, the entertainment center can be located at a far end of the design away from the house, so that nobody has to go to the kitchen. Since it’s essentially replacing the kitchen for people enjoying a dining patio nestled out in the landscape, it tends to have everything, including the kitchen sink. Refrigerators, storage, dishwasher, sink, grill, gas burners are fairly typical. Pizza oven, wok ring, tandoor…. the sky’s the limit. This option can get pricey, especially considering that the sink should be plumbed into the sewer, and that all this equipment tends to need both electrical and gas lines.
Then, there’s the hybrid – put the pizza oven out in the landscape where it can double as an outdoor fireplace (codes permitting), and keep the grill near the house for easy access.