There are many species of hydrangea, but the most popular one with blue flowers is Bigleaf hydrangea (H. macrophylla). This is the plant with huge flower clusters whose color can be pink or blue, depending on the soil pH (blue flowers in acidic soil, pink flowers in alkaline soil). Zone 6 or warmer gardeners can grow this plant successfully. But for Zones 5 and colder, this particular species does not flower reliably. The plant normally blooms on the previous year's growth, and because it breaks dormancy very early, its flower buds are often killed. The plant will often survive by sending up sprouts from the roots if it is killed back to the ground, forming a tidy little foliage plant but no blooms. Prune out faded flowers in summer. If the branches are pruned in the fall, winter, or spring, the next summer's flower buds will be removed, resulting in no blooms that year.