Athletes had to prove they had not served a doping ban following allegations of a state-sanctioned doping regime.
But the head of the International Olympic Committee says those who cheat will still face an uneasy decade of waiting to see if constantly improving technology catches them.
The International Olympic Committee had asked the individual sporting federations to decide whether Russians could compete in their sports.
It followed a report that found evidence of a four-year, state-run doping program.
Even as the Olympics began, the process was still in its final stages, but Russian Olympic Committee president Alexander Zhukov says Russia will have the cleanest team at Rio.
"Criteria for participation for the Russian team has been the toughest in anticipation of the Games, and not a single team except for the Russian team was given a requirement and criteria that those athletes who were banned in the past are not allowed to compete this time."
Many had called for a total ban of Russia from the Olympics and had criticised the IOC decision to leave the decisions to the sporting federations.
But IOC president Thomas Bach has defended the committee's action and issued a veiled warning to any of the athletes trying to cover ongoing doping activity.
He says dopers will never be able to feel safe because their drug samples will be stored for 10 years for further analysis whenever necessary.
"The message is clear: We want to keep the cheaters away from the Olympic Games. The message is clear: There is no place to hide for cheats, and dopers can never feel safe anywhere, because we're storing these samples and we will follow up on each evolution there in scientific research and testing methods."
Mr Bach says he can look into the eyes of any athlete who disagrees about Russia's participation in the Games because he has a clear conscience.
"I know that not only I but also the Executive Board members all have weighed all these arguments very carefully. We also know that we have the support of many, many athletes, that we have the support of the three continental athletes associations, that we have the support of the world Olympians associations."
Even as the debate continues, the cloud over the doping issue is not dominating the moment for others as the Games begin.
At the Olympic Athletes Village, Australian captain Anna Meares moved some of the Australian team to tears with a speech as the country's flag was officially unfurled.
Chef de mission Kitty Chiller says the mood among Australian team members is promising as the Games get underway.
"The vibe in the village is fantastic. A very simple thing that I asked team leaders and asked athletes to do is just, every time you pass someone in one of these uniforms -- especially a proper jacket -- in the village, to look up and say g'day.* And that's happening between sports, between officials. There genuinely is a fantastic feeling of support and respect."
Attention is also turning to the 2020 Tokyo Olympics, where five new sports have now been approved for inclusion.
Softball and baseball, skateboarding, karate, climbing and surfing have been added in an effort to attract a younger audience to the Games.
Australia was traditionally a strong medallist in softball when it was included in earlier Olympics.
