Cartridges are designed in cooperation with rifle and handgun designers. The gun designers decide what rate of twist is most likely to perform well for the cartridge given the expected bullet weights and lengths. If you are using a longer than normal bullet, your gun may not stabilize the bullet because rate of twist is too slow. In that case your options are to use a different bullet or to replace the barrel.
This is only a significant issue with a few cartridges. 223 is the most notable because the guns were designed for 55 grain bullets and some people want to use bullets significantly heavier than that for either target shooting or big game hunting.
When researching a cartridge, read up on its history. Was it designed for a 40 grain bullet while you're intending to use 60 grainers? Could be a problem.
When ordering a custom gun make sure the maker knows what bullet weights you intend to shoot so he can select the right rate of twist.