Can someone be tried and convicted of murder when there is no dead body?  The answer, as in much of the law, is "it depends."

To convict someone of murder, the prosecution must prove the defendant killed the victim.  This means there must be proof that the victim is in fact dead.  This is usually proven with the discovery and examination of the dead body. 

However, it may be possible to prove the victim's death in other ways.  For example, let's say the victim was last seen alone in her apartment on a Friday night, and the next morning, her apartment was found with a large pool of blood that matched the victim's  DNA, and she was never seen or heard from again.  That would be strong proof that she had died, even if the authorities never found her body.  It would be even stronger if an expert testified that the victim could not have survived after losing the amount of blood found.

Of course, there would still need to be evidence tying the defendant to the killing, but as far as the death is concerned, that could be proven even without a dead body. 

Without such strong evidence of death, the defense would likely argue that the victim simply ran away.  If there was no pool of blood in the example of above, but the victim was merely never seen or heard from again, the defense would have a good argument that no murder in fact occurred. 

I short, it is difficult to prove a murder case without a dead body, but not impossible.