Kanva dynasty was the successor of the Shunga dynasty in Magadha. They also known as Kanvayanas. They ruled for very short time duration of 45 years (75 to 30 BCE). Like Shungas, Kanvas were also from Brahmin origin. They considered themselves as decendents of Rishi Kanva. Vasudeva Kanva was the founder of the dynasty. He killed last ruler Devabhuti Shunga of Shunga Dynasty and ascended the throne.
During their time in north yavanas(Greeks) were became strong and occupied Punjab region. When Kanva Dynasty established their rule in Magadha, Shunga princes were still ruling in Vidisha. At the same time Satvahanas(Andhras) in south declared themselves independent under the rule of Simuka and started to attack Magadha. The Second king of the Kanva dynasty was Bhumimitra , who fought many wars against Satavahanas. After that Satvahana got busy with their internal problems and stopped attacking Magadha. Kanva rulers after Bhumimitra, ruled peacefully.
Bhumimitra succeeded by Narayana, who ruled for 12 years and then succeeded by his son Susaraman. Around 30 BCE Satavahana again attacked Magadha, this time they defeated last Kanva king Susharman and annexed their kingdom. This put to an end to Kanva dyansty as well as the Magadhan Empire.
Even though Satavahana conquered Magadha, it is not possible to assign them in the history of the Magadha, because the Satavahanas was originally ruling dynasty from Deccan. Did they ruled from Pataliputra for some time? Or political center of gravity shifted to Paithan (Capital of Satvahanas)? These questions were not satisfactory answered. But we know for sure that after the fall of Kanvas, name and fame of the Magadhan empire vanished from history for some time.