Oof, this is a very long story that I will try to tell as concisely as I can.

The USSR was a socialist state, and under socialism--at least in theory--the state owns everything. The state is controlled by the party, and thus control over the resources of the country is in their hands, particularly in the hands of those of high rank.

Now, humans being humans, the idea of the socialist planner selflessly directing the economy for the benefit of the masses turned out to be a fiction--many party officials had their hand in the till.

According to a popular joke, Leonid Brezhnev showed his mother around his home after becoming Premier. He showed her the garage, full of foreign luxury cars given to him by other leaders, the various perks and amenities he was afforded as Premier, and so on and so forth. After the tour, he asked his mother what she thought, and she said, "this is all very nice of course, but Leonid, what are you going to do if the Bolsheviks come back?"

This phenomenon would become a major point of contention between Soviet and Chinese socialists. The Chinese believed--correctly, in my opinion--that the Communist Party would generally tend to become the new bourgeoisie. The Chinese princelings of today bear out this theory, as many of them are either members of the Communist Party or at the very least well-connected to it.

Anyway, humans being humans, there is also an element of racism to this. Though the USSR was at least in theory a classless society, it did not eliminate differences among people, and someone growing up in a non-Russia (as in the ethnicity) SSR could expect to have fewer opportunities to rise through the ranks of the party. Indeed, one of the major destabilizing forces leading to the collapse of the USSR was the nationalities question, which had been inflamed by the Soviet-Afghan War, where the USSR made extensive use of soldiers from its Central Asian SSRs in a brutal, grinding war.

So, corruption in the metropole and fewer opportunities for people from outlying SSRs, aggregated over years, plus a collapse in oil prices, which revealed that a resource curse had been covering the decrepit state of Soviet industrial architecture. Add in some massive political dysfunction in Moscow, and we're all set for the collapse!

Which we're going to gloss over, because it's not central to your question. Or rather it is, but not in the way you think. The transition from a planned economy to a free market economy in Russia was not a thoughtful process seeking to maximize public welfare through the distribution of assets, slow withdrawal of subsidies, and the phased removal of trade barriers.

On the contrary, the transition was known as "shock therapy," and in a country where there was a long history of corruption and very little enforcement of laws under Yeltsin became a murderous sprint to see who could strip the country to the bone the fastest. In many cases, the murderousness was quite literal--many would be oligarchs were killed by their competitors for the same resource package. The Aluminum Wars are a well-known example of this, but similar efforts occurred in paper production and elsewhere. All the while workers who had expected the state--with its many, many flaws--to take care of them were often left out in the cold (again, literally).

Many of the "Oligarchs" we now identify with the heights of Russian wealth made their bones through violent /corrupt expropriation of state assets after the fall of the USSR. The chaos of those early years would stabilize under Putin, who basically married political power to wealth, using the former to check the latter when necessary, and ensuring that the latter backed the former in the person of Vladimir Putin and Vladimir Putin alone.

At some point over the past four years you may have heard of Oleg Deripaska in regard to his connections to Paul Manafort. He is basically this story in miniature. A go-getter under the USSR, his path to prominence vanished with the fall. He then made bank on the commodities market, eventually creating the Sibirsky Aluminum Group, which merged with another oligarch's holdings to become RUSAL (basically, "Russian Aluminum"), and managed to hold on despite allegations that he had various unhelpful parties, shall we say, *exit the market*, for which he has faced few consequences thanks to his cozy relationship with Putin.

Anyway, that's about as short as I can make the story. I hope it helps.