Heat the oil in a deep-fryer to 390°F (200°C). Dip the mussels, one by one, in the batter or coat with flour, shaking off any excess.
Carefully drop the mussels into the hot oil and deep-fry for a few minutes, until golden brown.
Fry only a few mussels at a time to avoid lowering the temperature of the oil.
Remove with a slotted spoon, drain, and arrange on a warm platter. Season with salt and pepper.
Garnish with lemon wedges and serve immediately with Tzatziki, Eggplant (Aubergine) dip, or Taramosalata.