As I understand things, I am one of those lucky people whose occupational pension derives from what is called a Fully Funded scheme: money is paid in and invested and the pension is paid from the yield on the investments. This is not the same as a guaranteed income: if the pension fund managers screw up on the investments, then the pension will be lower than anticipated, perhaps much lower. Mine supposedly keeps pace with inflation.
State pensions in the UK are not fully funded; far from it. They are basically paid from current taxation. And there lies the problem.
Older people are living longer but the birth rate is static or falling. The proportion of tax-paying workers relative to pension-receiving non-workers is falling. The burden of the old on the young will increase, perhaps intolerably.
It's just like a Ponzi scheme: you can only keep on paying out the old investors if new investors keep coming on board. You use the money provided by the newcomers to pay the money due to the older members. At some point, you run out of enough newcomers and the scheme collapses.
Working tax payers will expect some of their taxes to be spent on them and their children directly and on infrastructure. They don't want to see it all going to support the elderly.
Some governments - France, Russia - respond to the predicament by trying to raise the birth rate - that's equivalent to trying to drum up new custom for a Ponzi scheme. The evidence from France is that such encouragement to breed is not very successful.
Other governments - the British under New Labour - have welcomed young, single and usually male working migrants who boost the tax take but will hopefully go back to where they came from before they get old. Quite often, they do, but politicians know that immigration is an issue on which economic rationaility does not have the final word.
All governments are moving to raise the pension age. In Greece, they are starting from an amazingly low base (58). In the UK, from a historic five year discriminatory gap between female and male pensionable age (60 and 65). In addition, many public sector jobs have allowed early retirement - I was able to put up my hand to be "restructured" out and have had an occupational pension from the age of 50.
The point may come when governments may begin to think the unthinkable.
For example, they may decide to stop funding any research basically aimed at extending life expectancy. They may start charging older people for their prescriptions and their flu jabs. They may ration life-saving operations for those with only a few years to live anyway.
In other words, governments may try to damp down the seemingly inexorable rise in life expectancy. Actually, such a policy doesn't seem to me particularly cruel or unreasonable. There are limits to the burden the old should place on the young. And for many older people, living beyond 80 or 85 doesn't seem much fun.