Cybersecurity

In my logs I find entries about attacks on my system. I know IP addresses, I know date and time and I know what they tried to do. So what's the best I can do now? Tell everybody that there are cybercriminals on that network? Write an email to their admin? Anything else?

I would want to block the known attacking IP(s) on the firewall at the gateway into the network and the node that is being attacked.

If it was a hijack attempt, maybe let Spamhaus know.

The Spamhaus Project

You should block those IPs using firewall.
You should have strong password for root login, if that is ssh attack. Or even you can think about locking the root account, and use some sudo account to do the administration and be in the safer side.

While the advises above are valuable, I can also vote for contacting Spamhaus for such issues, if deemed they are proper for their activity. Having worked as Security and Abuse administrator, I can only say I was pleased to work with Spamhaus for a few years, but like I said, it will depend on the type of attack.

This question cannot be answered unless you describe the nature of the attack.

Your question is so vague, that we have no idea, really what you are talking about. A web attack? An SSH login attempt? A simple scan? Spam? What kind of attack?

Why would you ask such a question without providing any details and expect to get a useful answer?

Sorry.
To provide more details, with "attack" i meant SSH brute force - somebody tries to login as "Administrator" or with other users over SSH for many times. I think the IPs are always dynamic. To spam, what do you think of offers on the Web to subscribe for spam and of using it to spam spammers? Using email aliases, it would be possible. And, i didn't know (email) spam is considered as an attack.
To make my question in the first posting more precise: did I understand it right that for an attacker there will be no consequences?