If you're wondering, this drama does not follow the story line of the previous Hannibal film franchise. However, it does not mean that the series doesn't pack its own punch in terms of tension and suspense. (I'm in such awe, I feel inadequate trying to leave a review for this show. I won't reveal any more than what is available on the wikipedia page.)
Following protagonist Agent Will Graham (Hugh Dancy) into his mind and peering into the distorted lives and actions of serial killers, he comes across as a highly intelligent but often conflicted man, tormented by his own imagination and yet has to live it each day for the greater good.
This sense of vulnerability and instability caused by his personality (largely introverted and antisocial) is preyed upon by his psychiatrist, famed Hannibal Lecter, excellently portrayed by Mads Mikkelsen, and as all this is played out, the audience, privy to this knowledge will be gripped by suspense, and the never ending tension, even on scenes where nothing appears to be happening, the mood takes on a somber and tense tone.
For those who are concerned with the relative 'low level of gore', be patient. It takes its time to build and slowly escalate, bringing Graham deeper into the shadows and mental torment.
I can't emphasize how good the acting is, how vivid and artistic the abstract dream and killing sequences are. the fact that the soundtracks are well selected and not obnoxious all plays a part in creating one of the best viewing experiences ever. As a fan of psychological horror, I feel privileged to be able to take a small peek at this show ahead of broadcast.