If you divided your mature irises and transplanted young rhizomes, they may take two or three years to establish and bloom. The rhizomes haven't been able to create and store enough energy yet to produce flowers.
Irises need at least six hours of direct sun to bloom well; morning and early afternoon sun is best. If your transplants aren't getting enough, or if they have been planted against a white, south-facing wall and are getting too much, they may not flower at all. Transplanting to a place where they must compete with other plants or weeds for sunlight, water and nutrients, hinders blooming.
While irises don't benefit from high-nitrogen fertilizers, they thrive in soil that has been deeply amended with compost and well-composted manure. Doing so also will improve drainage and help avoid root rot. Without an adequate supply of nutrients, particularly phosphorus, irises will bloom lackadaisically or not at all. But if they are fed too much nitrogen, they'll grow foliage but no flowers. Use bone meal or bulb fertilizer in spring and early fall.
In mild climates, the top of the iris rhizome should be exposed to the sun, or planted so it is just beneath the surface of the soil in cold climates. Sometimes, mulch piles up around irises or they settle into the soil so the top of the rhizome gets covered. This impedes flowering.
Irises are amazingly drought-tolerant, but they won't bloom well if they need to struggle with drought while forming buds and blooms. Water them deeply when the weather is dry but let them dry between waterings. Overwatering increases susceptibility to fungal diseases and bacterial rot. Water irises at the base; avoid wetting their leaves.
A late freeze can stop the flower stalk from developing and damage iris foliage. Some irises are more affected by the weather than others and will bloom sporadically, rather than every year like clockwork.