Cartridges designed to fire this type of projectile typically deliver devastating speed and and shock-effect. The lower weight ranges of the projectiles are limiting the size of game and range at which you can effectively use these types of cartridges. These cartridges are regarded as excellent varmint and bird hunting calibers.
Cartridges in the 6 mm bullet class are very popular for target shooting and benchrest competitions in particular.
One of the most popular match calibers, the 6,5mm bullet has excellent aerodynamic properties and good sectional density which give it good ballistic potential.
The 7 mm is probably most famously shot out of the 7 mm Remington Ultra Magnum, but there are new and exciting additions like the Blaser Magnum that build on the fine heritage of german 7 mm calibers cartridges.
Perhaps the most widely used hunting bullet is the 30-caliber bullet, usually fired from a 308 Winchester or a 30-06 Springfield, but the options are endless. While these cartridges enjoy widespread hunting usage, there remains a strong community of competitive target shooters as well. The typical games that are hunted with a 30-caliber bullet fall into the medium game category, but even large herbivors like Moose are apropriate to hunt with this caliber.