Mahabharata is a great epic telling a story across multiple generations concluding with Arjuna's grandson Parikshit taking over the throne from Samrat Yudhishthira. Parikshit was the son of Abhimanyu, who was famously killed on the 13th day of the Kurukshetra war when multiple warriors set aside all the rules of the war and brutally killed the young man inside the Chakravyuha. 

Another famous son of Pandava was Ghatotkacha, the son of Bhima, who also died during the Kurukshetra war the very next day after Abhimanyu, when the battle continued through the night and eventually Karna had to use his one time use Indra's dart to put an end the carnage cause by the brave Ghatotkacha among the Kaurava ranks. 

These were not the only sons of Pandavas. While puranas mention many sons to each Pandava brothers, we will stick to the ones mentioned in the epic Mahabharata. We might cover the pauranik list in some other post some day. 

Sons of Draupadi - Draupadi had one son each from her five husbands, who were collectively referred as Upapandava. Prativindhya was Yudhishthira's, Bheema's son was Sutasoma, Shrutakarma was the name of Arjuna's son and Satanika and Shrutasena were the sons of Nakula and Sahadeva respectively. 

All the five Upapandavas participated in the Kurukshetra war and fought bravely alongside their fathers against the Kaurava army. They survived the 18 days of the war, however they were killed by Ashwatthama, when he attacked the Panchal camp at night and slaughtered everyone in the camp. 

Apart from the son of Draupadi, Mahabharata mentions few other sons of the Pandava brothers. 

Ghatotkacha - Ghatotkacha was the Rakshasa son of Bheema and Hidimbi, who was born through their union when Pandava brothers were hiding after escaping the fire at Varanavat. Despite being a Rakshasa, he got all the qualities of his father and remained devoted to his father and uncles throughout his life. 

He was present whenever his father needed him and in the end died fighting for Pandava in the Kurukshetra war. On the 14th day when the battle continued through the night, he being a Rakshasa became super powerful and caused a carnage in the Kaurava ranks and killed many Rakshasa from Kaurava side, who came to stop him. Eventually Karna had to use Vasavi Shakti of Indra, which he was saving to kill Arjuna, on him. Even in his death Ghatotkacha ensured death of many enemy soldiers by taking his giant form. 

Iravan - When Arjuna went on his personal exile after walking into Yudhishthira and Draupadi's chamber, he was kidnapped by a Naga women named Uloopi. Uloopi, who was a widow, insisted on marrying Arjuna. After a lot of persuasion by Uloopi, Arjuna finally agreed and together they had a son Iravan. Being born to Naga mother, he had all the magical powers of Nagas, which came in use when he decided to fight alongside his father in the Kurukshetra war.

Iravan was the hero of the 7th day of the war, when he and Ghatotkacha together caused massive damage to Kaurava army. He was killed on 8th day by Rakshasa Alambusha, who used his Rakshasi maya to counter Iravan's Naga powers. 
Barbuvahana - During his personal exile Arjuna met Chitrangada, the princess of Manipur. Chitrangada was the only child of her father so they got married on the condition that Chitrangada would stay in Manipura and their child will be the heir to the Manipura throne. 

This child was Babruvahana. Babru did not participate in the Kurukshetra war. He later faced his father Arjuna during Yudhshthira's Ashwamedha, and managed to kill him because of Ganga's curse. He was later revived by Ulupi. 

Abhimanyu - The most famous among the sons of Pandava was the son of Arjuna and Subhadra. He was almost as good an archer as his father and was instrumental in the Kurukshetra war.

When Drona created the Chakravyuha to capture Yudhishthira in Arjuna's absence, Abhimanyu stood up and broke into the formidable Vyuha. He was unstoppable all day and caused mayhem in the Kaurava ranks. Eventually multiple Kaurava warriors ganged up to kill him after Karna broke his bow from behind.