For a list of the sites that link back to you, use this kind of search in most search engines:
(some engines use the plural, some the singular)
For a list of the sites that link to you and that actually sent visits to you (a much smaller list usually) you can check the referrer field of your logs or the referrer report in an analytics package. I don't know what tumblr offers you. But the referrer information is poor quality anyway and will miss a lot.
As for what keywords you are listed under, there's no way to answer this. If, however, you have a list of keywords that you want to check, you can use a program such as WebPosition or a service such as Web Agent to search those keywords in various engines and report back to you on your site's rank for each keyword. But, as I said, you have to create the starter list. To make the list, start with vocabulary that your site already uses. That's really all the search engines do anyway.
If you want to know what terms get searched on and that are relevant to your topic, you can try WordTracker, and quite a few other suggestion tools including those offered by Google and Yahoo and so forth. These use a variety of algorithms and thesauri to come up with synonyms or associated terms.
You'll find more information in the search engine forums than this tracking forum.