How do I distinguish between 'binary' and 'text' files?

Informally, most of us understand that there are 'binary' files (object files, images, movies, executables, proprietary document formats, etc) and 'text' files (source code, XML files, HTML files, email, etc).

In general, you need to know the contents of a file to be able to do anything useful with it, and form that point of view if the encoding is 'binary' or 'text', it doesn't really matter. And of course files just store bytes of data so they are all 'binary' and 'text' doesn't mean anything without knowing the encoding. And yet, it is still useful to talk about 'binary' and 'text' files, but to avoid offending anyone with this imprecise definition, I will continue to use 'scare' quotes.

However, there are various tools that work on a wide range of files, and in practical terms, you want to do something different based on whether the file is 'text' or 'binary'. An example of this is any tool that outputs data on the console. Plain 'text' will look fine, and is useful. 'binary' data messes up your terminal, and is generally not useful to look at. GNU grep at least uses this distinction when determining if it should output matches to the console.

So, the question is, how do you tell if a file is 'text' or 'binary'? And to restrict is further, how do you tell on a Linux like file-system? I am not aware of any filesystem meta-data that indicates the 'type' of a file, so the question further becomes, by inspecting the content of a file, how do I tell if it is 'text' or 'binary'? And for simplicity, lets restrict 'text' to mean characters which are printable on the user's console. And in particular how would you implement this? (I thought this was implied on this site, but I guess it is helpful, in general, to be pointed at existing code that does this, I should have specified), I'm not really after what existing programs can I use to do this.

You can use the file command. It does a bunch of tests on the file (man file) to decide if it's binary or text. You can look at/borrow its source code if you need to do that from C.

file README
README: ASCII English text, with very long lines

file /bin/bash
/bin/bash: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), for GNU/Linux 2.2.5, dynamically linked (uses shared libs), stripped

You can determine the MIME type of the file with

file --mime FILENAME

The shorthand is file -i on Linux and file -I (capital i) on macOS (see comments).

If it starts with text/, it's text, otherwise binary. The only exception are XML applications. You can match those by looking for +xml at the end of the file type.