Absolute Galois groups have played a central role in most major breakthroughs in Algebraic Number Theory in the last half century.

Typically, the action of these groups is through an “almost pro-p quotient” with ramification at primes above p. For such groups the Poitou-Tate duality theorem is a powerful tool.

These theorems do not hold for pro-p groups unramified at primes above p. I will survey how this tame situation differs from the wild one above and introduce theorems of Labute and Schmidt which give situations where certain tame Galois groups have many nice properties and what our aspirations should be.