DSL is still used in Berlin? Over telephone lines?

telephone lines owned by the Government (Telekom, private in theory, owned by the Government on paper), no less!

there is some DOCSIS (cable) service, mostly from Vodafone but also a smaller provider named telecolumbus.

There was versatel, but 1&1 smartly purchased it at what I believe to be an absolute steal. They have what is clearly the widest fiber network reach outside of Telekom, and 1&1 is actually going out there and selling it.

I could, if I really wanted to, get 1Gbps symmetrical for only 500EUR/month. The catch is the ~3000EUR install and minimum 3 year commitment. but, at least the option is there. Telekom, if they have fiber "available" at your address, will offer you 20Mbps for around 700EUR a month, then do this really weird delivery of an STM-1 (155Mbps) circuit, broken out into E3s (45Mbps) to a Cisco ASR1002 (a 5000EUR device, easily), that is converted to a rate limited GigE interface. Oh, and the install fee is about 1200EUR and takes a solid six weeks...but only if you call every day to remind them.

Berlin internet connectivity is a sick and twisted joke.

This reminds me my conversation with a salesperson in a Deutsche Telekom retail shop in Berlin. The fastest DSL in my apartment was 6 Mbit/s. No VDSL available because "all sockets are taken" probably by the neighbours or by the business on the ground floor - the guy was literally blaming their shitty connection on my neighbours. I was this close to killing him with the chair he was sitting on.

Yes, in all German cities. Usually 100Mbps down, 40Mbps up via DSL. That’s what I’m using myself, too.

Currently work is being done to upgrade the phone network to 500/200 in the next years.

I didn't know that it's possible to do 100Mbps on telephone line. Last time I used DSL, there was 8 Mbps down and 1 Mbps up, but practically much less.

xDSL is still used in most places. It generally works well and the infrastructure has been in place for a long time, which is the reason broadband has become so accessible. Fiber is gradually replacing it, but it's a major investment to lay fiber. So xDSL is going to be around for a long time, especially to deliver broadband to customers for whom fiber doesn't make economic sense.