Double-click a two-gigabyte log and TextEdit beachballs. Vim opens it, eventually, and then every search crawls. Nothing is wrong with the file - the problem is that editors are built to edit, so they read the whole file into memory before showing you the first line. For a log you only need to read, that work is wasted twice: you wait for it, and you pay for it in memory.
Here is what actually works, from fastest-to-try to best-long-term.
Option 1: less in Terminal
less is on every Mac and opens files of any size instantly, because it reads only what it shows:
less /path/to/app.log/pattern searches forward, n repeats the search, G jumps to the end, q quits. For a quick look at a big file, this is the honest baseline - and if the log came from a terminal with color codes in it, less -R will even render them.
The limits show up when you go past looking: a search jumps match to match, but you cannot collapse the file to just the matching lines, keep their line numbers, or eyeball severity while scrolling. less shows you the file; it doesn't help you read it.
Option 2: cut the file down first
If you already know what you are looking for, extract it before opening anything:
grep -n "ERROR" app.log > errors.logor split the file into pieces any editor can handle:
split -b 200m app.log chunk-Both work, and both cost you the file: the extract has no surrounding context when you find the line that matters, and the chunks have no line numbers in common. You end up back in the original anyway.
Option 3: a viewer that never loads the file
Log Viewer is a free Mac app built around one idea: the file is memory-mapped, never read. A two-gigabyte log opens as fast as a two-kilobyte one, memory stays flat while you scroll, and there is no size limit that comes from the app. Then the reading tools are already there - filter a million lines down to the handful that matter with their real line numbers kept, severity colored so errors are visible while scrolling, and Follow for a file that is still being written.

It's free on the Mac App Store, with no accounts and no network access - the log never leaves your Mac.
FAQ
Why does TextEdit take so long to open a large file?
It reads the entire file into memory and builds an editable document from it before showing anything. That's the right trade for editing a letter and the wrong one for reading a gigabyte of logs.
Can Console.app open large log files?
Console is built around the Mac's unified system log. It can open plain log files, but it isn't designed for arbitrary multi-gigabyte files, and it offers no filtering that keeps your place in the original.
Is there a file size limit?
In Log Viewer, none that comes from the app: it maps the file rather than reading it, and draws only the lines on screen.