We certainly don't need to tell you that there's nothing worse in this world than getting caught with your pants down. To literally avoid such embarrassments, gentlemen throughout the ages have employed a series of technologies ranging from braided fiber cords to $12,825 alligator skin belts clasped with diamond-encrusted 14-karat gold buckles. Along the way, the stylistic development of men's trousers has come to be inherently intertwined with the curious evolution of these sartorial restraining devices -- as the fabric and cut of men's pants has frequently changed according to the available means of securing their fit. The responsibility of keeping modern men properly covered isn't one solely shouldered by the belt, however. Since at least the time of the French Revolution (a period often noted as the genesis of what's come to be understood as 'modern men's fashion') braces (or suspenders) have also played an important role in augmenting present-day menswear.
In their early French incarnation, braces (or 'bretelles') were simply formed from ribbons draped over the shoulders and secured to the waistband with buttons. But as braces proved more and more useful and comfortable -- by helping to loosen the snug-fit of gentlemen's waistbands without letting their wearer down -- their designs became more formalized. With the likes of Benjamin Franklin and Mark Twain both famously weighing-in with their own designs, patents, and preferences in the manufacture of these fashionable items, braces were here to stay.
For what it's worth, the finest braces haven't strayed too too much from their earliest design. High fashion still dictates that the best fit (and look) is achieved from silk braces secured by buttons sewn on the inside of the waistband (note that buttons appearing outside the waistband should only be worn under a full-length vest). Metal-clasped suspenders, invented in 1894 and popular with more casual looks and usages, can notoriously damage waistbands, appear sloppy (or bulky) from beneath a jacket or vest, and should typically be avoided by the modern gentleman.
All this said, it's seldom that one sees the suspender outside of very formal occasions these days. The story of the suspender's suppression typically maintains that in the particularly sweltering summer of 1893 most men were driven to give-up their braces and to opt for belts so they could avoid perspiring under the straps -- and, well, the rest was history. Soon belt loops became standard elements on men's pants, waistbands slid down the frame and started to rest more on the hips, and the suspender seemed to have been banished solely to the realm of white or black tie events.
The belt's tyranny hasn't been quite that absolute, however, and renowned tailors and men's outfitters alike have long still offered suspender secured pants as an alternative to those anchored with a belt, and fashionable men have continually turned to such garments as a way of diversifying their wardrobes, or generally setting their suits apart from the standard business-uniform.
In acquiring your own braces, just remember that, like any fashion accessory, there are certain rules to be followed in wearing them. First, foremost, and as stated above, one should always avoid metal-clasp braces and should only wear leather buttoners. Second,your suspenders will be the first thing someone notices after your tie and/or pocket square -- so remember that these items need to work with (and not against) one another and should be matched accordingly (although they need not be identical fabrics). Third,lighter color straps should typically be worn with lighter suits and darker colors should respectively be paired with darker suits, for formal occasions black braces should be worn with your tuxedo, while white braces are meant for evening tails. Fourth, remember that while etiquette doesn't deem that the leather ends of your braces need to match your shoes (as with belts) -- many men do choose to do this; ultimately its a matter of taste. Finally, remember that braces are worn as an alternative to a belt and not in addition to one. This last rule may seem obvious, but you'd be surprised by what you sometimes see on the streets.