Many molecules are moved through the body by .

Many molecules are moved through out the body by PROTEINS.
Proteins carry out several functions in the body. They serve as enzymes, they are involved in production of hormones, they produce energy, they form antibodies and they are involved in transportation of molecules round the body. The proteins that are involved in transportation are called carrier proteins. Carrier proteins facilitate the transportation of diverse particles via the plasma membrane into the inside of the cells. 

The answer to this question would be: protein.

The membrane of cells wasn't permeable to many kinds of molecules. That is why there are some canal and channel that make the transport of those molecules possible, even with a higher gradient of concentration. The canal and channel itself made by protein.