Because there’s a lot of variation in quality, it helps to know what to look for when shopping for shrimp.
The best shrimp are flash frozen in blocks of water like giant ice cubes within hours of pulling in the net. This is the best way to preserve the flavor and texture of the shrimp—it seals the shrimp and prevents it from getting freezer burn. If you can buy a block of shrimp from your fishmonger (usually 4- or 5-pound blocks), that’s the best way.
Your next best bet is buying frozen unpeeled shrimp in a bag and thawing it yourself. Your grocery store or fishmonger will have bags of frozen shrimp. If you don’t see them, ask. Most likely, this shrimp has been individually quick frozen (IQF) and is just as fresh as the ice-block shrimp, just not as protected from freezer burn. So check for excessive ice crystals.
Unless you live where shrimp is caught locally, the shrimp that’s beautifully displayed at the fish counter won’t be fresh; it will have been previously frozen and conveniently thawed for you—but the problem is that you don’t know how it was thawed, nor for how long. If this appears to be your only option, take the time to ask: The store may have some of the very same shrimp in the back that they haven’t yet thawed. Ask for that instead.