One of my E-mail addresses used to get 20,000 to 100,000 spams a day, but it was around for a long time (since the 1990s.) I still have the domain, but since there is no way to deal with such a deluge, the domain is all but shut down due to that.
The latest generation of spammers are using links to websites which will infect/compromise a computer the second they visit the site, usually through older Flash, Java, Acrobat, or other add-on exploits. Some sites even will try to attack Android devices (by trying to get you to download a bogus "securityupdate.apk" file.) If the first round of exploits doesn't work, there is always phishing or asking someone to download a "PDF" which is actually a "pdf...exe" file, and is a Trojan horse.
The newest attacks are pretty nasty. Ransomware is quite profitable these days, as well as attacks that fry actual computer hardware.
As usual, my solution is to have the web browser in a sandbox, VM, or both. I have had malware try to get out of a sandbox by creating billions of small files and directories (which does a number on the filesystem), so I like using both solutions. This way, something that completely freezes the sandbox can be just rolled back to a safe snapshot.