How can I conditionally format cells to denote past/future/current dates?

I have a church rota Google Sheet. Column A shows the date of each service.

To make it more obvious at a glance, I would like cells in column A to apply formatting so that dates in the past are colored differently. Ideally, the next upcoming date would be highlighted (or at least dates in the current month or something like this).

I am somewhat familiar with conditional formatting but not using it on dates – is this feasible and if so how can I do it? In a perfect world, the entire row would be colored for past weeks but just the cell is sufficient if this is getting tricky.