The review is based on the investigation results of features and generation conditions of various non-linear phenomena in the high-latitude ionospheric F-region induced by the extraordinary polarized powerful HF radio waves. It examines the following: (1) artificial field-aligned irregularities (AFAI); (2) ducts of enhanced electron density; (3) narrowband (± 1 kHz of the heater frequency) stimulated electromagnetic emission (NSEE); (4) HF-induced Langmuir radio-induced and ion-acoustic plasma waves; (5) radio-induced optical emissions (RIOE) in the red and green lines of atomic oxygen. Features of non-linear phenomena induced by the ordinary (O-mode) and extraordinary (X-mode) HF pumping were compared, including non-resonance phenomena excited at high effective radiated power (ERP > 300 MW), when the pump wave is not reflected from the ionosphere. Prospects for development of research on ionospheric modification by powerful HF radio waves in Russia are briefly considered.