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Government Processing Times
Processing times vary not only by the type of application, but by the facility where the application is being processed and often by the basis for the application. An H-1B may take less time through the Vermont Service Center than the same case would take through the California Service Center, while an I-140 Immigrant Visa Petition filed with the Nebraska Service Center based on Labor Certification may take less time than an I-140 filed in the same place based on Extraordinary Ability.
In many cases, it may not be possible to track a specific case online. Rather, the date of receipt of cases on which the various agencies are currently working can be viewed instead. This will provide information concerning whether the agency in question has reached the case you are checking, but not how long it will take to complete processing or what the outcome will be.
U.S. Citizenship and Immigration Services Processing Times
USCIS provides a way to check on individual cases here, if they were filed at a Service Center and if you have the case's Receipt Number (a ten-digit number preceded by EAC, LIN, WAC, TSC, or MSC). The letters and all ten digits must be entered. Another page, accessible here, allows you to select a local District Office or Service Center and view the date of receipt on which the selected office is currently working for the various types of applications.
U.S. Department of Labor Processing Times
The U.S. Department of Labor has several resources online for determining the progress of pending cases. Permanent cases filed under the new PERM system can be status-checked by the employer filing the petition if they sign on here. Attorneys currently can check only if the employer has created a sub-account for them (also needed for the attorney to prepare and file the case initially).
U.S. Department of State Visa Availability and Passport Processing
The U.S. Department of State has a page available here from which you can link to the chart of available visas by preference classification (click on the "Current Bulletin" link; separate tables are available for Family- and Business-sponsored cases).
If you are a U.S. citizen processing a passport application, information on the status of your application is available here.