Thanks for the links and the repsonses.

Increasing the blocksize limit is a possible short- to midterm solution and it's increasingly discussed so this might be undertaken in the near future. I imagine a blocksize of 10 MB is possible thus increasing the limit to 70tr/s. This is already quite impressive and should be enough for a couple of years.

But:

Bigger blocksize does not only increase the storage requirements but also the time other miners verify a block and thus the risk of producing an orphan block. I've not yet heard of a solution how this might be circumvented.

I think the longterm solution IF Bitcoin becomes a transaction currency instead of a speculation object is more off-blockchain transactions. How to make those secure and reliably integrated in the main blockchain will be a challenge.