Why is there no cure or vaccine for the common cold?

The common cold is caused by a variety of viruses such as rhinovirus and coronavirus. These viruses are small and simple consisting of little more than genetic material and a few proteins. Because viruses replicate so rapidly, their genetic material undergo mutations readily. With these mutations, the virus’ genetic material and proteins change enough to appear like a brand new virus. Therefore, because the viruses that cause the common cold are so simple in structure and so apt to have mutations, vaccines and host immunity are virtually impossible.
On the other hand, the influenza virus (causing seasonal flu) is a larger virus with proteins and genetic material that are essentially conserved; its mutations occur much less often than the viruses causing the common cold. Therefore, we are able to isolate and vaccinate for specific strains of flu each season.