There are several aspects of twig.js that can be extended with custom functionality.

They are:

1. Functions
2. Filters
3. Tests
4. Tags

Custom functions can be added through Twig.extendFunction(name, definition)

For example, a function that repeats a value could look like:

Twig.extendFunction("repeat", function(value, times) {
    return new Array(times+1).join(value);
});

And you can use it in a template like:

{{ repeat("_.", 10) }}
{# output: _._._._._._._._._._. #}

Custom filters can be added through Twig.extendFilter(name, definition)

For example, if you wanted to add a filter that reversed words in a sentence, you could do the following:

Twig.extendFilter("backwords", function(value) {
    return value.split(" ").reverse().join(" ");
});

Then, in your templates you can use:

{{ "a quick brown fox"|backwords }}
outputs: fox brown quick a

Custom filters with arguments are also supported:

Twig.extendFilter('catify', (value, args) =>
  args.reduce(
    (newString, toCatify) => newString.replace(toCatify, 'cat'),
    value
  )
);

{{ "the quick brown fox jumps over the lazy dog"|catify('fox', 'dog') }}
outputs: the quick brown cat jumps over the lazy cat

See Extending twig.js with Custom Tags