The monokini is at the same time one of the most alluring and one of the most impractical swimsuits ever concieved. In its traditional form, it's like a modified bikini bottom with two straps that theoretically cover the breasts and connect or tie behind the neck. The drawback of this is that it offers very little support at the top, and so cannot readily be worn by those with ample endowment. See sundress.
When worn by someone with the appropriate figure, however, the monokini is quite possibly one of the sexiest articles of clothing ever designed. Something about the way its contours complement those of the bearer make for a knock-out combination. Around the turn of the 21st century it has become a popular outfit choice for figure competitions, and is starting to show up in more and more mainstream clothing suppliers.
There is also a variation on the bikini that is often called a monokini. In this version, the front of the bikini bottom has an extension tapering up toward the bust line, usually connecting to a ring between the cups. Though it has a level of stability equivalent to the bikini (such as it is), it doesn't quite have the same visual potency as the one-piece version. However, diversity is a good thing.
The very first version of the monokini was in some ways more intelligent. It consisted of a very modest bottom which just covered the belly button, and two spaghetti straps that tied behind the neck. It was designed by Rudy Gernreich in 1964 and modeled by Peggy Moffat. This version left the bust completely bare; in fact, its intention was to "free" the bust. Were this original monokini to succeed, the world would probably be a better place.