You can search the full text of hundreds of journals in the combined databases available in LexisNexis and Westlaw. (Bloomberg Law also has law journals, but its coverage is much more recent than Lexis or Westlaw.)
The Current Index to Legal Periodicals (CILP) indexes journals received in our library. It often picks up new articles before they appear on Lexis or Westlaw. UW Law students, faculty, and staff can subscribe to CILP or to its tailored version, SmartCILP, to get weekly email updates.
HeinOnline has the full text (and PDFs) of hundreds of journals. Its coverage goes back much further than that of Lexis or Westlaw—generally to volume 1 of each journal. If you are writing about a case that was decided six months ago or a statute that was just enacted, that early coverage might not be important to you. But for many topics you will want to know what scholars said years ago.
Note that HeinOnline's search connectors are a little different than Lexis and Westlaw's. Check the user guides.
The Index to Foreign Legal Periodicals (available on HeinOnline and linked from the law library's homepage) indexes journals that are not from the U.S., U.K., Canada, or Australia. It also indexes journals from those countries if they focus on international or comparative law. And it indexes some book chapters.
If you are writing on a topic focused on state or federal law, you probably will not need to check IFLP, but if you topic is comparative or international, you should.
If your topic crosses disciplines, you should check indexes from outside law. For instance, if you are writing about health and human rights or about privacy in genetic information, see whether there are relevant articles in public health or medical journals. Depending on your topic, you might check indexes for business, economics, political science, history, or other fields.
An excellent way to find relevant databases is to visit the University Libraries Research Guides page.
The UW Libraries catalog gives you several options for searching. The broadest option, "Articles, Books + More," searches about 20 indexes, as well as library catalogs. With one search you can find books in the law library, books in other campus libraries, dissertations, and articles from many journals.
For example, searching for irs surveillance privacy turned up (in the first screen) articles from a law journal, a computer trade journal, a business magazine, and a newspaper.
Searching indexes as part of a catalog search can be a good, quick way to get a sense of the range of material on your topic.
But it is not as focused as searching an index directly. That is, if you know that you want sociology articles, you have more options using Sociological Abstracts than you do having Sociological Abstracts as one of many indexes searched as part of "+ More" through the catalog interface.