Blue whales are the largest mammals, and possibly the largest animal of any kind to have lived on Earth. A 33-metre long, 190-tonne whale has been seen, but most are smaller than this.
Blues were hunted to the brink of extinction during the 20th Century, before being protected in the mid-1960s.
The most recent abundance estimate for the Southern Hemisphere is 2,300 and there is evidence they are increasing annually by about 7%.
There are no good estimates for numbers in other areas, but there is some evidence of a population increase in the North Atlantic.
The fin whale is the second-largest whale species after the blue, to which it is genetically close. Fin-blue whale hybrids are known.
There are no agreed estimates of current total population, although there are some signs of recovery in parts of the Southern Hemisphere where it has been protected since 1976.
There are about 40-50,000 in the North Atlantic.
Japan and Iceland have caught the fin again in recent years, with Iceland awarding itself quotas of 154 per year. Greenlandic aboriginal hunters target 10 per year
There are three recognised species of rights. By studying the genetics of parasitic whale "lice", scientists estimate the split ocurred 5-6 million years ago.
They are so called because they were the "right" whales to hunt - slow, swimming close to shore and would float when killed.
The right whale has been protected since the 1930s, although illegal Soviet whaling took large numbers in the North Pacific and Southern Hemisphere up to the 1970s.Two of the three species are on the brink of extinction.
Fewer than 400 are believed to exist in the North Atlantic, while the North Pacific species may be slightly more numerous. The Southern Hemisphere species numbers about 8,000 to 10,000.
The fast-swimming sei whale was caught in great numbers in the Antarctic in the 1960s, after the blue, fin and humpback stocks had been overexploited.
Japan has issued a permit to take up to 100 sei whales in the North Pacific for research.
There are no agreed estimates of current numbers in the Antarctic. In 1989, the North Atlantic population was estimated at 10,500, and claims have been made for numbers ranging from 9,000-28,000 in the western North Pacific.
It has been protected since the late 1970s in the Antarctic and North Pacific, and since 1982 in the North Atlantic.
Made famous in Moby Dick, sperm whales have been hunted since the 17th Century.
It is the only "great whale" with teeth. Sperm whale oil once lit the lamps of the major cities of the US and Europe; and after WWII, 30,000 a year were being caught. They have been protected since 1982.
There are no agreed current estimates of number. Some authors believe the historical population worldwide may have been 1-2 million, and that there may now be 360,000-1 million.
Japan has issued a scientific permit to take up to 10 sperm whales in the North Pacific.
The bowhead is a single species - closely related to the right whale - and is remarkable for being the only baleen whale to spend all its time in Arctic waters. The bowhead's huge, bony skull allows it to break through the sea-ice.
There are thought to be more than 17,000 in existence. The bowhead is a target for indigenous hunters in Alaska, Chukotka and Greenland who are allowed to catch no more than 69 individuals a year under IWC rules.
Bryde's whales are found mainly in tropical or subtropical seas. They were long confused with sei whales.
There are no agreed estimates, although there are thought to be about around 25,000 in the western North Pacific.
They were only exploited in any numbers towards the end of the commercial whaling period in the early 1980s just before the moratorium came into place.
Japan's scientific whaling programme will take up to 50 Bryde's whales a year in the western North Pacific.
One of the best known whales because of their distinctive flippers and tail flukes, their acrobatic "breaching", and for the singing males on the breeding grounds.
Once heavily exploited, the humpback has been protected since the mid-1960s and is increasing in many parts of the world.
There are probably now more than 30,000 in the Southern Hemisphere, 15,000 in the North Atlantic and 18,000 in the North Pacific.
Four whales per year can be taken by aboriginal subsistence hunters in St Vincent and the Grenadines, and an annual quota of nine was recently agreed for Greenland.
There is a single species of gray whale split between two populations in the Pacific.
The western North Pacific gray is one of the most endangered in the world, numbering about 130.
The eastern Pacific gray, by contrast, has recovered to its pre-exploitation levels of about 20,000.
The eastern gray is famous for its epic migration which takes it from the cold Bering and Chukchi seas to the warm waters of Mexico to breed and calve a round trip of 20,000km.
No more than 140 eastern grays a year can be taken by US and Russian subsistence hunters.
The two species of minke are the world's most hunted whales. Japan has been targeting about 950 a year for its research programmes, though its immediate plans are unclear.
Commercially, Norway issues quotas to hunt about 1,000 per year, while Icelandic boats catch up to 216 per year. Greenland's Inuit hunters can take up to 190 for subsistence purposes.
Estimates of minke numbers for the Southern Hemisphere are currently under scientific review, but there are probably more than 450,000.
There are more than 145,000 in the North Atlantic and about 25,000 in the western North Pacific.
The man who saved thousands of Jews then disappeared
Playpens to drones - new ideas to reduce deaths by drowning
Great long reads to enjoy at your leisure
What could you buy for the cost of a Super Bowl ad?
Does technology make people touch each other less?
- Phoenix Nights's Ted Robbins 'stable' after onstage collapse
- Japan outraged at IS 'beheading' of hostage Kenji Goto
- Nicky Morgan announces 'war on illiteracy and innumeracy'
- Whitney Houston's daughter 'found unresponsive' in bath
- Newspaper review: Innumeracy war, and the 'four-year-old rapist'
- Greece economy: PM Tsipras seeks to placate creditors
- Missing Samantha Henderson: Body in lake had head and neck injuries
- Super Bowl ads: What could you buy for the cost of a commercial?
- Japan wakes up to bad news about Kenji Goto
- General election 2015: Labour promises 'no PM pictures'