Balarama famously taught both Duryodhana of the Kauravas and Bhima of the Pandavas the art of fighting with a mace. When war broke between the Kauravas and the Pandavas, Balarama was equally affectionate to both parties and so decided to be neutral. Eventually when Bhima (of greater strength) defeated Duryodhana (of greater skill) by dealing a blow below the navel with his mace (a move against the rules of mace combat), Balarama threatened to kill Bhima. This was only prevented when Krishna reminded Balarama of Bhima's vow to kill Duryodhana by crushing the very thigh he exposed to his wife Draupadi.
In the Bhagavata Purana it is described that after Balarama took part in the battle that caused the destruction of the rest of the Yadu dynasty, and after he witnessed the disappearance of Krishna, he then sat down in a meditative state and departed from this world. In some accounts it is described that a great white snake left Balarama's mouth at this point in reference to his identity as Ananta-Sesha. And the place where he departed from this world is situated about 1 km far from Somnath Temple in Gujarat. There is one cave at that place and the white snake who came out of Balarama's mouth got into that cave and went back to Paatal Lok as the local people of Veraval say.
Balram does not know the love affair of Arjun and Subhadra. He happily announces the marriage he has fixed for his sister Subhadra with Duryodhana and asks all to be happy. Subhadra on hearing this news faints.
Subhadra is now crying, and Rukmani consoling her. Arjun wants to get out and leave; and the tragic scenes build up.
Krishna is unmoved and when questioned by Rukmani; gives a practical solution which she understands and which they follow. Subhadra goes to worship the Goddess; and here in she calls upon Arjun; and then drives the chariot herself so that it is now a kidnap but a willing go for Subhadra with Arjun.
On getting this news; Balram is angry and wants to take revenge with Arjun. When Krishna makes him understands the situation, Balram agrees and ultimately grants the wedding. The wedding is then carried out between Arjun -- Subhadra at Dwarika.
Balram in his anger takes some wrong decisions which Kanha sorts out and sets them right and here also
In CB Balram is challenging Kanha to defeat BH as a human being which Kanha accepts but very intelligently Kanha puts a condition he will only turn to God when Balram himself asks him so lets wait and watch what that situation will be