The story of Yusuke Urameshi, thoughest of his school and a juvenile delinquent who doesnt care about life. One day while walking down the street a young boy chases his soccer ball into the street, and just as about he is to be runover Yusuke jumps in to save his life, this resulting in Yusuke's death. Being considered a "bad apple", no one expected Yusuke's sacrifice in the spirit world so there is no place for him and he is offered the opportunity to return to life. The opportunity consists of going through a test to revive and if succesful becoming a spirit detective: an agent who solves problems for the spirit world on the human world. Reluctant at first, after attending his funeral Yusuke decides to take the test and being succesful, he revives as a spirit detective.
The first arc consists solely of Yusuke being sent on missions as a spirit detective, in which he gathers Kuwabara, Hiei and Kurama as allies and Genkai as his master. At the end of first arc Yusuke meets the Toguro brothers, which invite him to the "dark tournament" to face off once more. Yusuke and co. enter the tournament with the aim of taking down Team Toguro. Afterwards happens Chapter Black which introduces former spirit detective Sensui and the psychics, and finally the 3 kings saga which introduces Makai and its rulers.
Yu Yu Hakusho overall is quite a strong verse, its power is divided in classes and give a pretty clear scale for the power in each tier. E classes are the bottom of the bottom of demons and humans who have no or barely any spiritual power. D classes has clearly superhuman fighters (although not very impressive overall). C class showcases higher levels of power with beings in the hypersonic range and being around building buster level. B class is where things start to get impressive with casual large building busters up to town+ (possibly hill) busters and double digit mach speeds. A classes had little showcasing, but are stated to be several times stronger than any B class and an A++ level threat could potentially wipe out Japan. S class is extremely vast as it is above anything that the spirit world can handle, S classes are stated a few times to be able to wipe out the world (likely refering to wiping out everything on the planet, not destroying the planet itself since there are no feats that would imply planetary destruction). The power of S classes can greatly vary, but even a low tier S class like Sensui are a threat to the world (calced at continent level). Top tier beings are over 40 times higher in power level than Sensui, and can break through his durability with the air pressure launched from a simple flick of there finger. The peak of Yu Yu Hakusho is hundreds to thousands of times the speed of sound and more than likely continent level in power.
In YYH there are 3 known worlds/dimensions, all filled with powerful fighters, specially Makai (the demon world) which is filled with B and A class demons, and even a considerable amount of S classes. It is also worth mention that the spirit world has a cross dimensional cannon which can shoot at pretty much any target designated on the world and destroys everything in a 50 kilometer radius.