I've been at companies where we receive hundreds of applications per role posted, and one where we receive 10s. I've posted about this before but in both cases the pipeline was the same - initial pass eliminates about 70-80% of the candidates because they're just not worth following up on - think things like IT staff applying for mid level development jobs with no experience, education or anything to indicate they could write any code. Of the remaining we end up filtering out based on comparing applications - this bit sucks, but pretty much stack ranking the resumes and picking out the top 20 or so[0]. At that point, everyone gets a phone screen with a set of questions picked from a list and we proceed through that. The same process works mostly because the size of your interviewing group scales with the number of engineers you hire.

[0] side note - I work in games where we're often filtering resumes for specific roles, e.g. a gameplay programmer or an online programmer. The filtering here is most of the time bucketing candidates based on their experience and sorting that way.