> Can someone explain to me how the US has jurisdiction over Credit Suisse?

Because the US is a sovereign state, which means they have jurisdiction over whatever they choose to have jurisdiction over, subject to constraints forcibly imposed by outside parties.

> I see how they could have gone after the individual tax fraudsters (American citizens), but how can they police foreign banks?

The US government (even ignoring extraordinary action it could take outside of the US or with the cooperation of foreign governments) can effectively impose penalties on any entity that does business in the United States, or holds assets in the United States.

Or because they have branches and accounts in the US:

https://www.credit-suisse.com/us/en/

>impose penalties on any entity that does business in the United States, or holds assets in the United States.

Or even does business with US citizens.

They are foreign banks operating in the United States, so they have to also obey US laws.

Not only that, but if they want to conduct business with American banks, or just hook into the system, they are subject to certain pressure from the US government. E.g. dealing with Iran or DPRK is a nono.

IANAL but I think the alternative for Credite Suisse is to stop doing business with the US and US-based companies.

What others said (operate in US = must obey US laws0 AND the fact that they can freeze out any bank out of the US financial industry.