General Brazilian
bairro de periferia / periferia
Most common usage throughout Brazil; 'periferia' alone is often used as shorthand
Rio de Janeiro
favela / bairro de periferia
Favela is commonly used for the poorest peripheral areas; bairro de periferia for more established outlying neighborhoods
São Paulo
periferia / bairro periférico
Both terms widely used; periferia is extremely common in São Paulo's sociological discourse
Portugal
bairro periférico / arredores
Less commonly used; Portuguese prefer 'arredores' (outskirts) or 'bairro de habitação social'