Athletics' world governing body has banned Russia's athletics federation over claims of state-sponsored doping.
But the Russian Olympic Committee and 68 athletes, including two-time Olympic pole vault champion Yelena Isinbayeva, have taken their case to the Court of Arbitration for Sport (Cas).
The Olympics Games start on 5 August.
Russia was suspended from global track and field events by the International Association of Athletics Federations (IAAF) in November 2015.
That followed the publication of an independent World Anti-Doping Agency (Wada) report that showed a culture of widespread, state-sponsored doping, with even the secret services involved.
The country's sports minister, Vitaly Mutko, has since apologised for the fact cheating athletes were not caught by Russia's anti-doping systems but stopped short of admitting the scandal had been state-sponsored.
