The Snappi diaper fastener is made from a stretchable non-toxic material, which is T-shaped with grips on each end. These grips hook into the diaper fabric to ensure a snug-fitting diaper with enough natural movement for the baby. We weren't sure how well it works, but found this rave review at Cool Tools (which also warns against inferior knock-offs).
Snappis are also available in toddler size.
Available in a variety of colors at Amazon. Prices start at $1.69 per fastener.