During 2013, tropical cyclones formed in seven major bodies of water, commonly known as tropical cyclone basins. They were named by various weather agencies when they attained maximum sustained winds of 35 knots (65 km/h; 40 mph). Throughout the year, a total of 141 systems formed, with 89 of them being named. The most intense and deadliest storm of the year was Typhoon Haiyan, which had a minimum pressure of 895 hPa (26.43 inHg) and at least 6,352 deaths in the Philippines, while the costliest tropical cyclone of the year was Typhoon Fitow, which caused damages amounting to $10.4 billion in China, becoming its costliest typhoon (in nominal terms) at the time. Among this year's systems, twenty-one became major tropical cyclones, of which five intensified into Category 5 tropical cyclones on the Saffir–Simpson scale (SSHWS). The accumulated cyclone energy (ACE) index for 2013 (seven basins combined), as calculated by Colorado State University (CSU) was 618.5 units overall, which was below the 1981-2010 mean of 789.0 units globally.

The most active basin in the year was the Western Pacific Ocean, which had 30 named systems, including one system that crossed from the Central Pacific. The Eastern Pacific Ocean had an above-average and destructive season, with 20 named storms forming; many of its systems were weak and short-lived; nine of those became hurricanes, and only one strengthened into a major hurricane. The North Atlantic had a total of 14 named storms; two of those became hurricanes. It was the first year since 1994 with no major hurricanes, Category 3 or higher on the Saffir–Simpson scale, and the first in the satellite era where no hurricanes reached Category 2 strength. The North Indian Ocean was active, with five named storms forming, producing the fourth-most accumulated cyclone energy in this basin on record. Activity across the Southern Hemisphere's three basins (South-West Indian, Australian, and South Pacific) was fairly significant, with the regions recording twenty-one named storms altogether, with the most intense Southern Hemisphere cyclone of the year, Cyclone Bruce in the South-West Indian, peaking with a central pressure of 920 hPa (27.17 inHg).

Tropical cyclones were primarily monitored by ten warning centers across the world, which are designated as a Regional Specialized Meteorological Center (RSMC) or a Tropical Cyclone Warning Center (TCWC) by the World Meteorological Organization (WMO). These ten centers are the National Hurricane Center (NHC) and the Central Pacific Hurricane Center (CPHC), Japan Meteorological Agency (JMA), Indian Meteorological Department (IMD), Météo-France (MFR), Indonesia's Meteorology, Climatology, and Geophysical Agency (BMKG), the Australian Bureau of Meteorology (BoM), Papua New Guinea's National Weather Service (PNGNWS), the Fiji Meteorological Service (FMS), and New Zealand's MetService. Unofficial, but still notable, warning centres include the Philippine Atmospheric, Geophysical and Astronomical Services Administration (PAGASA), the United States's Joint Typhoon Warning Center (JTWC), and the Brazilian Navy Hydrographic Center.

The El Niño–Southern Oscillation stayed in its neutral phase throughout the year, with no major fluctuations towards either an El Niño or La Niña event. However, during May and June, sea temperatures in the far eastern tropical Pacific Ocean were well below average. By October, though, they returned to normal.

The 2013 Atlantic hurricane season was a very inactive season, featuring only two hurricanes and no major hurricanes.

The 2013 Pacific hurricane season featured nine hurricanes, including Hurricane Manuel, the second costliest Pacific hurricane on record.

The 2013 Pacific typhoon season was the most active season since the 2004 season, deadliest since 1975, and featured Typhoon Haiyan, one of the strongest tropical cyclones to ever exist.

The 2013 North Indian Ocean Season was the most active since 2010 and 2007. It also featured one of the most intense tropical systems to make landfall in India - Cyclone Phalin.