a) Ramakrishna mission with its Advaita focus
b) Yoga practice (mainly through the disciples of Krishnamacharya
c) The westernized variant of Gaudiya Sampradaya - ISKCON
But it is basically the three forces I mentioned
Since then there has been zero outreach in my view from India to the west.
Is that a good or a bad thing?
The Ramakrishna Math represented a "modern" monastic order in late 19th cen, with a mission that was outward looking
To me it is a tad unfortunate...that this outward looking zeal has practically died out in Hinduism, and Indian society...
And what's worse, one does not see any signs of revival
That you don't really have any Hindu voice influencing the western cultural climate in any meaningful way
So all serious discussion of Hinduism in the West is actually done by western scholars