The seismicity of the Earth is described briefly, together with the largest earthquakes in XX century and the most destructive known earthquakes in the world. Schema of the tsunami generation mechanism is shown and the most destructive tsunamis in years 1850-2000 are listed. Two strong earthquakes and tsunamis, the greatest in the modern world, the Lisbon earthquake of 1 November 1755 (over 60,000 casualties) and Sumatra-Andaman earthquake of 26 December 2004 (about 300,000 casualties) are described. Finally, some problems of earthquake and tsunami monitoring in the context of tsunami warning system are discussed.