Sinn Fein leader Gerry Adams famously said about the IRA that "they never went away, you know", and researching the current BBC World Service series, After the KGB, left me with a very similar impression.
Vladimir Putin joked he had infiltrated government for the FSB
As the BBC's Moscow correspondent in the late 1980s and early to mid-90s, I witnessed the collapse of the Soviet Union and the outpouring of popular hatred for the regime's notorious secret police.
I was in Lubyanka Square in front of the KGB's headquarters on 22 August 1991, as demonstrators toppled the statue of Feliks Dzerzhinsky, the organisation's founder. When a hawser was tied round Dzerzhinsky's neck and the 14-tonne colossus came crashing to the ground, it seemed the KGB's days were numbered.
The new President, Boris Yeltsin, moved to neutralise the secret policemen by cutting their budget, slashing their numbers and hiving off their functions to rival agencies. He renamed the organisation the FSB - Federal Security Service - but somehow the spirit of the KGB lived on.
In the political and economic chaos of the Yeltsin era, thousands of disillusioned agents went into the private security business.
Dima Fonariev, a KGB bodyguard for Mikhail Gorbachev who set up his own security firm, says private sector pay in the 1990s could be 10 times higher. A burgeoning crime wave also meant security expertise was in high demand.
"They were crazy days. So many dead bodies, so many guys who simply disappeared. I remember this time because I was invited to work for a guy who wanted me to carry a Kalashnikov. But I said 'no, no it is against the law!'"
Not all the former agents shared Mr Fonariev's scruples. Some became involved in organised crime. Within a few years, former and serving security men had replaced the mafia in running the country's thriving protection rackets. Some were caught up in even darker activities.
Mikhail Trepashkin, an ex-KGB-colonel who remained in the service, worked closely with Nikolai Patrushev, who is now the head of the FSB. Mr Trepashkin won a medal for uncovering illegal arms sales by FSB agents to Chechen militants, but when he began to probe deeper into connections between FSB officers and criminal groups, he found himself ostracised and his investigation blocked.
FSB poster: The spirit of the KGB lived on in the new organisation
"In Moscow, several times, we arrested armed men who were preparing terrorist acts, and then they were released! It made no sense to me at all. So I decided to compile a report for our leadership in the FSB to establish why this was happening. My report went to Nikolai Patrushev, who was then working on internal FSB affairs. I got no reaction.
"Then, in 1995, I had definite information about an FSB employee who was working in a criminal group, kept a weapons store, and killed people. When I wanted to catch that group Patrushev gave the order for those documents of mine to be destroyed."
Eventually Mr Trepashkin himself was arrested. A gun was planted in his car and he was charged with the illegal possession of firearms. He successfully contested that charge, but was then accused of disclosing state secrets and sentenced to four years in a labour camp. When I spoke to him he had just been released from the prison.
Despite Yeltsin's efforts, the FSB remained stubbornly unreformed and determined to regain its lost power. In 1999, Vladimir Putin, then director of the FSB and a career KGB man, was appointed prime minister.
Ex-KGB-colonel Mikhail Trepashkin spent four years in a labour camp
On 20 December 1999, at an FSB party to celebrate the founding of the Cheka, the Bolshevik secret police, he told his former colleagues: "Dear comrades, I can report that the group of agents you sent to infiltrate the government has accomplished the first part of its mission."
The second part of the mission - getting a KGB man into the presidency - was accomplished the following year.
Under Vladimir Putin, the security services have regained their former prestige, their budgets and their numbers are now higher than ever, and they have gained positions of power in all areas of the nation's life.
According to research by the Russian Academy of Sciences, three quarters of senior politicians have a background in the security forces and Russia's largest companies are now headed by former KGB men with personal ties to Vladimir Putin.
The Kremlin argues this is a good thing - that Russia needs a strong hand to restore order. When I spoke to President Putin's spokesman, Dmitry Peskov, he was reassuring.
"The majority of [former KGB men] are very talented and very skilful people. They are just people like us - they are not aliens," he said.
But there have been suggestions that some of the new politician-businessmen have abused their positions to enrich themselves. Individual branches of the FSB, each controlled by a politically powerful patron, have been involved in turf wars over corrupt business schemes. One of them led to an armed showdown on the tarmac of a Moscow airport.
When he was elected, Mr Putin declared war on the wheeler-dealer businessmen, the so-called oligarchs who snapped up the country's massively lucrative state industries in the economic meltdown of the 1990s.
Many of them were dispossessed and their assets, counted in the billions of dollars, were taken over by state corporations, most of which have a former KGB man in charge. Mr Putin's former colleagues now head up the country's oil, media, railways and armaments industries as well as the state airline.
It would be wrong to say the bad old days are back in Russia: the security services are no longer the monolithic instrument of state repression they were in the darkest periods of the Soviet Union.
But they have become rich and powerful, and whereas the Soviet KGB was always tightly controlled by the Communist Party, their modern equivalents are increasingly becoming a law unto themselves. The new president, due to be elected next month, will inherit a secret police that is in danger of becoming a state within the state.
The first part of Martin Sixsmith's two-part documentary, After the KGB, can be heard on the BBC World Service on Friday 22 February. Part two will be aired on 29 February.