Tooth cavities, or dental caries, are not a thing of the past. In fact, they are on the rise due to people's use of bottled water. The widespread use of fluoride toothpastes reduced dental caries significantly and is the reason most people 55+ have their teeth in their mouth and not on the nightstand (in the form of denture). Cavities are caused largely by acid-producing bacteria that resident inside biofilms attached to teeth (dental plaque). With the protection of the biofilm covering, the acids etch (demineralize) teeth leading to cavities. The body has no natural way of clearing biofilms from teeth. We can prevent their overgrowth by brushing and rinsing with an effective antimicrobial paste and rinse, but these daily procedures don't reach below the gum line and between teeth, so regular visits to the dentist and/or hygienists are needed to remove plaque, tartar and calculus from teeth. Fluoride helps remineralize teeth and helps stop demineralization causes by acids from bacteria and from diet (coffee, soft drinks, acidic foods). Fluoride can be toxic in large amounts. Children under 3 shouldn't be using a fluoride toothpaste. Beyond that, fluoride toothpastes are generally safe. If you get fluoride from flouridated water, you ingest 100%. If you get fluoride from toothpaste, you ingest less than 10% by inadvertent swallowing. The US FDA sets standards for fluoride toothpastes, as do equivalent agencies in many countries, so toothpastes are safe and effective ways to combat dental caries. In addition, the American Dental Association tests and evaluates fluoride-containing oral care products; look for the ADA Seal of Acceptance as further indication of a product's effectiveness and safety. In sum, dental cavities have not gone away. In fact, they are on the rise in adults 55+.

I agree with Jim Ratcliff
Although dental hygiene and care has improved immensely, I can't say for certain from personal experience that cavities are a thing of the past.
My children's dentist still recommended toothpaste with fluoride and also to use a fluoride rinse (like Listerine but sickly sweet fruit flavored).