The catastrophic earthquake of 8.1 magnitude on the Richter scale that took place on the morning of 19 September 1985, killing 9,000 to 30,000 people, remains fresh in the memory of the majority of Mexico City's inhabitants. Since the city was established on the dry bed of lake Texcoco and several geological faults that originate in the Pacific coast reach the city, earthquakes are a common phenomenon. Right after the 1985 earthquake, many constructions were reinforced and new buildings are designed to meet structural criteria by law and no major building collapse has happened since, even after several strong earthquakes. You can check the latest earthquake activity at the National Earthquake Centre an institute of the National University (UNAM).
Should you happen to be in the middle of an earthquake, remain calm and follow some simple rules: if you are indoors, stay under the doorways, move away from objects that can fall, and/or follow exit paths ("Rutas de Evacuación") out to the streets; if you are outdoors, move away from slopes or electrical wires towards open areas or marked "safe zones."