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The Crewneck
Typically worn with: A T-shirt underneath; you can wear it with a collared shirt, too, but it can look a little square.
Positively associated with: Athletes
Negatively associated with: Yuppies
Beware of: Thinking you can wear it without a collared shirt under a jacket. You can’t.

The V-Neck
Typically worn with: Collared shirts, including polo shirts (with the shirt’s collar tucked into — yes, into — the sweater).
Positively associated with: Laid-back weekends
Negatively associated with: Casual Fridays
Beware of: A plunging neckline. Never show more than the top two shirt buttons.

The Cardigan
Typically worn with: Anything from a T-shirt to a dress shirt and tie. A good cardigan is often a suitable way to add warmth on chilly fall days.
Positively associated with: Mr. Rogers
Negatively associated with: Fusty English professors
Beware of: Losing a button. And never tuck a cardigan into anything.

The Turtleneck
Typically worn with: A tweed blazer or a sport coat. You should also feel free to wear it on its own.
Positively associated with: Steve McQueen in Bullitt
Negatively associated with: Steve Jobs (His are cotton. But still.)
Beware of: Anything too tight or fitted. Or too loose and long, for that matter.