There are hundreds of species, in the Mediterranean and around the world. In Italy, it's officially a gambero if longer than 10cm (a prawn in the UK, shrimp in the US).
If less, it's a gamberetto (shrimp in both British and American English). A really big one is a gamberone, or king prawn (or jumbo shrimp).
In Italy there is also a freshwater cousin, a small crayfish called gambero di fiume, or gambero turco, gambero d'acqua dolce, or gambero di Galizia. Scheggino in Umbria is famous for them.
And they are presented in myriad different ways: in antipasti; gamberi con carciofi (artichokes) is a popular one. The same combination appears in risottos. A favourite on pasta, often paired with other seafood, or asparagus or zucchini.
gamberetti di nassa: difficult to catch in nets, the parapendalo or narwal shrimp (Plesionika Narval) are traditionally caught in handmade creels on the Amalfi Coast and are listed in the Ark of Taste.
gamberi imperiali: mazzancolle or tiger prawn
nuvoletti di gamberi are Chinese shrimp (prawn) crackers
Images by: Giovanni Bianco