A high-strength, cold rolled, annealed steel sheet (I) has composition (by weight, excluding iron, processing impurities and various optional components) 0.10-0.25% carbon, 1-3% manganese, at least 0.010% aluminum, up to 2.990% silicon (provided that Si + Al is 1-3%), up to 0.015% sulfur, up to 0.1% phosphorus and up to 0.008% nitrogen. The microstructure is 15-90% bainite, the remainder being martensite and residual austenite. A cold rolled, annealed steel sheet (I), with strength more than 1200 MPa, has composition (by weight, excluding iron and processing impurities) (i) 0.10-0.25% carbon, 1-3% manganese, at least 0.010% aluminum, up to 2.990% silicon (provided that Si + Al is 1-3%), up to 0.015% sulfur, up to 0.1% phosphorus and up to 0.008% nitrogen and optionally (ii) 0.05-0.15% vanadium, up to 0.25% molybdenum, up to 1.65% chromium (provided that Cr + (3 x Mo) is at least 0.3%) and up to 0.040% titanium (provided that Ti/N is at least 4). The microstructure is 15-90% bainite, the remainder being martensite and residual austenite. Independent claims are included for: (1) the production of (I) with elongation at break more than 8% from a steel as above, by (A) casting a semi-finished product from the steel; (B) heating to more than 1150[deg] C; (C) rolling to give a hot-rolled sheet; (D) coiling the sheet; (E) cleaning the sheet; (F) cold rolling the sheet at a degree of reduction of 30-80%; and (G) reheating the sheet at 5-15[deg] C per second to a temperature of Ac3 to Ac3 plus 20[deg] C, maintaining the temperature for 50-150 seconds, cooling at more than 25[deg] C per second to a temperature between B s and M s minus 20[deg] C, maintaining this temperature for 150-350 seconds and cooling at less than 30[deg] C per second to ambient temperature; and (2) the production of (I) with elongation at break more than 10% by a variant of the process, involving steps (A) - (G) as above except that (1) the steel contains more than 0.005% molybdenum, more than 0.005% chromium and no boron and consists of 65-90% bainite, the remainder being islets of martensite and residual austenite, and (2) in the reheating step (G) the sheet is cooled from the temperature of Ac3 to Ac3 plus 20[deg] C at more than 40[deg] C per second to a temperature between M s plus 30[deg] C and M s minus 30[deg] C (the holding time at this temperature and further cooling being as above).