The defendants - one Afghan and three Bulgarians - walked into the court room packed with journalists and onlookers, accompanied by police wearing face masks.
The refugees from Syria, Iraq and Afghanistan - 59 men, eight women and four children - were found crammed into the small, unventilated vehicle, abandoned on the side of a motorway in Austria.
Let our news meet your inbox. The news and stories that matters, delivered weekday mornings.
The deaths shocked Europe as it struggled to cope with the biggest influx of migrants since World War Two.
"The 71 victims due to the small space, inability to move, a lack of air and overheating ... died shortly after they set off on the journey. Before their death they continuously banged on the walls of the lorry and shouted," the court said in a statement before the hearing.
It was the worst incident seen on the overland route across the Balkans, where hundreds of thousands of people were making their way from the Middle East, Africa and southern Asia up to the richer countries of western Europe.
The trial is taking place in Hungary as authorities say that is where the refugees died, at the beginning of their trip into Austria.
The four defendants are also charged with trafficking other migrants over several months alongside seven other men. Only six of those, all Bulgarians, appeared in court in the Hungarian city of Kecskemet. Authorities said the seventh was still on the run.