Unlike most of Mr Putin's key advisers, who tend to hail from the president's home city of St Petersburg, Mr Shoigu was born in a small village on the Russian-Mongolian border.
Despite leading the Russian military for more than a decade, Mr Shoigu never served in uniform, rising through the ranks of the Communist Party before becoming the head of Russia's emergency ministry in the 1990s.
Mr Gerasimov, the third figure in this rivalry, is the ultimate army insider. He cut his teeth putting down a bloody rebellion in Chechnya in the 1990s, and is now the longest serving post-Soviet military chief.
Prigozhin's growing importance in projecting Russian power - and his group's ability to poach top special forces operators from the military by offering higher wages - are believed to have created tensions between the men for several years.
But it's really after the Russian invasion of Ukraine - and in particular post the bloody fighting in the meat grinder of Bakhmut, the battle where thousands of Wagner troops are believed to have been killed - that Prigozhin's hatred for the military elites has come to the fore.
The attempt to seize Bakhmut - a small city with a pre-war population of around 70,000 people - is puzzling. Most observers believe that it has limited military significance and some say the campaign was designed by Prigozhin to allow him to claim credit for a victory amid the military's faltering campaign.
He regularly accused Mr Shoigu and Mr Gerasimov of "constantly trying to steal [credit for] Wagner's victory" in cities like Soledar, where thousands of paramilitary troops - often recruited from prisons - met their deaths.
And by contrast to his more bureaucratic rivals, Progozhin's often foul-mouthed rants made him a personality that often caught the attention of the world's media. Leaked documents suggested that the Russian defence ministry was unsure of how to combat his messaging and increasing popularity.
In this regime, Mr Shoigu is kept in check by Wagner, while the mercenaries remain cowed by the military. At the top of the pyramid sits Mr Putin, the chess master moving pieces around the board and maintaining balance in the system.
Meanwhile, Prigozhin has always been careful to avoid criticising the president directly, instead suggesting that Russia's litany of failures since the invasion in February 2022 were due to Mr Putin being misled by his commanders.KG娛樂城
For Mr Putin, it was useful to allow the mercenary boss to pin the blame for the failing military campaign on underlings. The Russian president is believed to have privately criticised Shoigu and Gerasimov for the slow pace of the invasion.
But in recent months, Mr Putin's long held strategy has appeared to fray.
Prigozhin - increasingly irate over his suspicion that the military was withholding ammunition from his forces as they attempted to complete the capture of Bakhmut - began posting more and more unhinged Telegram rants.
In one video - with the remains of dozens of dead Wagner fighters visibly surrounding him in the background - he raged: "You [expletive] who aren't giving us ammunition, you scum, you will eat their guts in Hell!"
"Shoigu! Gerasimov! Where is the... ammunition?... They came here as volunteers and die for you to fatten yourselves in your mahogany offices," he yelled in another video, seemingly attempting to blackmail Moscow by threatening to pull his forces off the front lines and abandon the fight for Bakhmut.