Hydrangeas are flowering plants that come in a variety of sizes, from ground covers to tree-sized. They produce large clusters of flowers in blue, pink, white and occasionally yellow. They are a prized landscape element that has few pests to contend with. Two of those pests actually chew holes in the leaves or flowers.
The rose chafer is in the beetle family and feeds on a number of flowering plants, including hydrangeas. It feeds particularly on flowers as well as leaves and some fruits, leaving large, irregularly shaped holes.
Many caterpillars can be responsible for chewing holes in hydrangeas, but the leaf tier or celery tier moth's larvae are noted specifically as pests of the hydrangea by the University of California-Davis' Extension service.
Insecticides are one option, but so is hand picking the pests from the plant. The problem with spraying insecticides is that it will get onto the flowers and harm the beneficial pollinators that visit like honey bees.