An orange wedge is for juice, not oil: it sits on the rim of a Garibaldi, a Madras or an Eastern Sour so the drinker can squeeze a last burst of sweet orange into a drink that is built on it. A twist gives aroma, a wheel gives looks, a wedge gives something to do with your hands.
What is an orange wedge, as a garnish?
An eighth of an orange cut pole to pole, with a strip of peel along the back and a point of juicy flesh, notched so it perches on the rim. It belongs on drinks that have orange juice in them and could take a little more: the Garibaldi (Campari and fluffy orange juice), the Madras (vodka, cranberry and orange), the Eastern Sour (bourbon, orange, lemon and orgeat), the Screwdriver, the Tequila Sunrise, and the breakfast drinks. It also goes on long drinks where orange is a flavour rather than an ingredient, such as a rum and cola or an Aperol Spritz, where Italy uses a slice or wedge rather than a twist. The wedge is the most casual of the citrus garnishes: a wheel is for show, a twist for the oil, a wedge for juice, and you can tell a bar's intent by which it chooses. Navel oranges are seedless and juicy and the right choice; Valencias are juicier still but have seeds; blood oranges make a wedge that bleeds red into the glass.
How to use it
Trim both ends of the orange, halve it lengthwise, and cut each half into four wedges along its length; trim the white pith from the inner edge and flick out any seeds. Make a small cut in the flesh so it sits on the rim. Hang it on the glass for the drinker to squeeze, or squeeze it over the drink and drop the shell in. On a Garibaldi, the wedge is traditionally squeezed in and the shell left; on a Madras, it is squeezed and discarded. A wedge can be dipped in sugar for a sweet rim, or in salt for a Mexican-style highball. Wedges keep a few hours covered in the fridge and dry out by the next day; cut what you need. For a wheel instead, cut thin cross-sections and float or press them to the glass.
Substitutes
An orange wheel or half-wheel, for the look without the squeeze. An orange twist, for aroma in a drink that does not want more juice. A blood orange wedge for colour. A lime or lemon wedge on a vodka or tequila highball. A slice of orange in a spritz, which is the Italian way.
Cocktails with an orange wedge
The Italian one: the Garibaldi. The vodka one: the Madras. The bourbon one: the Eastern Sour. Every drink that takes an orange wedge is listed below, and most of the drinks under orange slice would take one instead.
Questions
Wedge, wheel or twist? Wedge for a squeeze of juice, wheel for show, twist for the oil. A Garibaldi takes a wedge; a Negroni takes a twist.
Do I squeeze it in? On a juice-based highball, yes; that is what it is for.
Which oranges? Navels: seedless, juicy and bright. Blood oranges for a red wedge in winter.
How many wedges per orange? Eight, cut lengthwise.
Can I cut wedges ahead? A few hours, covered in the fridge; they dry out overnight.
Does an Aperol Spritz take a wedge or a slice? A slice in Italy, a wedge in most bars abroad; both are fine, and both are meant to be squeezed a little.
What about a sugared wedge? Dip the flesh in sugar for a Sidecar or a Brandy Crusta; it turns the wedge into a sweet to finish on.
Finished with Orange Wedge.
3 recipes
Eastern Sour
Bourbon, orange, lemon, orgeat and sugar, shaken over crushed ice. Trader Vic's 1960s bourbon sour with almond — the Mai Tai's idea…

Garibaldi
Campari and fresh orange juice, whipped to a foam. Named for the man who united Italy — bitter from the north, oranges…
Madras
A Madras combines vodka, orange juice and sweetened cranberry juice over ice for a citrus-forward long drink finished with an orange wedge.