New Delhi, Aug. 14 -- Every year, before flying from the UK to visit family in India, 10-year-old Ziya Shah's aunt asks her if she'd like anything. This year, instead of chocolate or toys, Shah had a different request: make-up.

Shah doesn't have an account on Instagram or Facebook and uses YouTube with parental controls, yet beauty finds its way into her world through friends, online advertising and everyday conversations. "My best friend loves make-up, so I wanted to try it too," Shah says.

Her mother recalls being taken aback when Ziya recently suggested she try a hair-growth serum from a particular brand after seeing an advertisement online. "She declared that my hair is thinning," she says. "The real issue is the volume of targeted ...