We definitely still teach tables! I'm a Y4 TA, and it feels like times tables are my life right now! We're teaching a table per half term at the moment - they should know 10s, 5s, 2s, 3s and 4s coming up from Y3, and then we do 8s, 6s, 7s, 9s, 11s and 12s (in that order). Every child has a target table, and I have to have three pieces of evidence of them knowing their table (2x verbal, and one written piece of evidence) to move them up. There's a small intervention group (bottom set, essentially) maths group who are mostly on 2s and 5s, but the rest of the class are all 3s and above (big knot on 4s, and handful of 8s and 6s, a little cluster on 9s, and two on 11s).
I also run times table interventions with small groups about once a week - they love the times table game show, which pits two teams against each other in three different "games" to test their times table knoweldge. Ours also all have bookmarks with their target table on (they get a new one when they move up, and they get to keep the old one), with a little note to parents on the back asking to help them practice tables out of order, should have quick recall (not counting on their fingers), and also asking to practice related division facts. You can definitely tell when they've been practicing at home. I also have "ask me" stickers which I give them if there's one particular fact they're having trouble remembering, so they walk round all day with "ask me: 6x7=" stuck on their jumpers, and everyone they pass asks them.