Pistorius has admitted shooting Ms Steenkamp, 29, in the early hours of 14th February 2013, through a locked bathroom door.
The prosecution allege that the killing was premeditated, and that Oscar shot his girlfriend after a row, but the Paralympic athlete claims he mistook her for an intruder in his home.
27-year-old Oscar, who just six months before the tragedy had won gold at the Paralympics in London, is a double amputee after having his lower legs removed when he was a toddler.
He has been nick-named 'Blade runner' for the prosthetic curved blades he uses when sprinting. He is so fast on his prostheses that he competed against able-bodied athletes in the Olympics.
Pistorius appears in court today on the first day of what is thought to be a three-week-trial. Reeva's mother, June Steenkamp, is also in attendace, as well as several members of Pistorius's family.
This morning neighbour of Pistorius Michelle Burger has appeared in court to give evidence, recalling that: 'Just after three I woke up from a woman's terrible screams.'
Saying: 'She screamed terribly and she yelled for help. Then I also heard a man screaming for help. Three times he yelled for help.'
Ms Burger lives 177 metres from Pistorius's house and had her windows open on the night in question.
However, Ms Burger was also asked by the court why it took her a few days after the incident to come forward with her evidence, to which she replied that once she has heard other witnesses had come forward.
Pistorius maintains that he had got out of bed and rushed to the bathroom because he believed there was an intruder in his house and was trying to protect Reeva. He claims he had assumed Reeva was still in bed at the time.
The trial continues.