Son of Vegeta and Bulma, Trunks is only an infant when he first appears in DBZ during the Android Saga. He has purple hair like his grandfather Dr. Briefs, but his facial features, stance and strong Saiyan pride clearly show that he is a descendant of the Saiyan royal line. He has a sister named Bra who is about 12 years younger than he is. His role becomes much larger by the Buu Saga, at which point Trunks is 8 years old and fantastically strong for his age. He goes Super Saiyan while training with Vegeta in the gravity room, an event that comes as a shock to all considering his young age. Filled with pride, Chibi Trunks is adventurous and constantly looks for stronger opponents to challenge, much like his father. During the final episodes of DBZ, Trunks, who is now 18, appears to be developing the same personality as Future Trunks. He can be seen as adult Trunks throughout GT as well. Trunks is born in the year 766 AD, and is 29 years old by the end of GT.
Bra, Vegeta and Bulma's second child, is see for the first time in the end of DBZ. Her father doesn't appear to make a point of encouraging her to train (like he does to her brother Trunks), but the two are quite close, as it becomes apparent in GT, where Vegeta proves to be very protective of his daughter. Bulla loves her father very much and has a strong sense of pride in him.
Trunks (Mirai no Trunks, Future Trunks)
The son of Bulma and Vegeta He is around 18 when he first appears in DBZ to stop Frieza from destroying Earth. He is from the future and has witnessed a threat to Earth which cannot be stopped in that time. He has come back in time to try to save the Earth of his time, only to find our heroes in Earth facing their own peril. Much to the amazement of our friends, Trunks immediately turns Super Saiyan and defeats Frieza and King Cold. He gives Goku medicine to prevent his death from heart disease and tells them of Earth's coming predicament. The Z Fighters immediately go into training, and Trunks returns to his own time. Trunks returns to our timeline again in the Android Saga to ensure that the Androids do arrive on Earth and are stopped. He is also born during this saga, so we have the opportunity to see him both as a teenager and a baby at the same time. He continues to exist as a boy and a teen until the end of the Cell Saga, when the older Trunks returns to his original timeline and we see the baby grow up in DBGT.