The terms "formal," "semiformal" and "black tie" have been replaced by more nuanced and relaxed codes. You still don't want to be over- or underdressed, though, and deciphering the newest terms can be as challenging as translating a new language.
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Upscale restaurants, resorts and even parties may state the dress code as "casual elegance." This description is largely up for interpretation, but you definitely know it's not a tuxedo or floor-length gown. On the flip side, it's far more formal than flip-flops and a T-shirt. How you interpret a call for casually elegant dress largely depends on where you're going to wear it.
For a party or restaurant, upgrade up your normal "casual" attire into something just shy of dressy. For men, this means a streamlined look with dark colors -- such as a charcoal or navy suit or slacks with a corresponding blazer and button-down shirt. A tie is optional, but a belt and dress shoes -- no sandals or sneakers -- are musts.
Women might wear a pants suit or a little black dress with a cardigan or scarf. Separates are also appropriate, as long as they look put together; a dress skirt with a turtleneck or silk blouse fit right in. Dressy heels or flats and neatly styled hair complete the look.
A resort or cruise interpretation of casually elegant might feel a little more loose and fun. A button-down shirt, pressed jeans or shorts and dress shoes can outfit a man, while a woman could wear a maxi dress or a skirt with a flowing blouse. Color and whimsical patterns may make an appearance, but flip-flops, bathing suits and cut-offs are definitely out.