I know this thread is old, but I was struggling with the same question, so I’ll post the answer in case anyone else comes across this thread like I did.

tl;dr:

• form_for should no longer be used and will eventually be removed from Phoenix.
• In LiveView, use <.form for={@form}> where @form is a Phoenix.HTML.Form struct (generally created using to_form). Don’t use :let.
• Outside of LiveView, you can also pass a changeset or map to for, and it’ll be converted to a Form which can be captured with :let. (This approach is also technically possible in a LiveView, but it’s discouraged because it makes change tracking less efficient.)

The second and third points are made clear in the docs for form/1. The first point was confirmed to me by none other than Chris McCord; I wrote about it here:

Correct. .form is the way to go, form_for will forever exist for backwards compatibility, f = form_for is deprecated and should be rewritten.

I found some answers in the Phoenix.HTML docs:

1. <%= f = form_for @changeset ... %> is now deprecated. Use <%= form_for @changeset ... %> instead.

2. <.form> is a “function component”, in the context of Phoenix LiveViews.

This leads me to a follow-up question: If I don’t use LiveViews, should I still use <.form>?