They have a long history, dating back to ancient Rome, and were called Ovis Apalis. These dressed eggs or stuffed eggs were seasoned eggs flavored with spicy sauces and served as a meal starter.
Hard-cooked eggs were so popular with the Romans that they would say “ab ova usque ad mala,” meaning “Eggs to Apples,” from the beginning of the meal to finish with the apples at the end.
The name deviled implies hot but need not be. It is simply hard-boiled eggs chilled and halved with the yolk whipped into a flavorful filling of various flavors such as mayonnaise, sour cream, yogurt, Dijon mustard, etc.
Spice it up with cayenne, hot sauce, or wasabi. Add fresh herbs like dill, cilantro, or chives; it's a nice touch.
Make special occasion up-end garnishes such as chopped prosciutto, crisp chopped pancetta, or with a sliver of smoked salmon, sour cream, and caviar. The name deviled implies hot but need not be.