A while ago my Wordpress-based personal site was hacked with SEO spam. I've since cleaned it up (removed and reinstalled wordpress, manually checked through all files, manually checked database entries). The scan at https://sitecheck.sucuri.net/ now shows the website to be OK (before cleaning, it showed that there was SEO spam). The Sucuri and Wordfence plugins indicate that the site is clean. So I'm pretty confident that I've cleaned the website completely.
Now, the problem I face is that the Google results for the site still show lots of SEO spam, which obviously doesn't look very good. This is the same for DuckDuckGo and possibly other search engines. How do I go about cleaning that up? Are there any active steps I can take to do that, or do I just have to wait for their crawlers to recrawl the site and update the search results?