Extensive experimental and theoretical research has been performed in the last decade to study ionospheric irregularities. These studies have shown that plasma instabilities play a major role in the generation of the irregularities. In this work we describe in detail the recent experimental studies of the E and F region irregularities and also the extensive work on plasma instability theories developed to explain them. We also describe both radio wave and spacecraft-borne experimental techniques to allow a common ground for the understanding of the data from ground-based and in situ experiments. To date, theoretical work has been mostly concentrated on the low-latitude irregularities and, together with computer simulations, has been able to explain many aspects of the experimental data. These theoretical efforts are also discussed in some detail. The role of neutral winds in the creation of large-scale ionospheric structures such as mid-latitude sporadic E is beyond the scope of this review.