AbstractThe history of whaling is very largely one of repeated over‐exploitation of the various whale stocks which became available through discovery or technological advance. Modern whaling has similarly caused considerable reductions in the numbers of some species in the major whaling grounds.Stock assessment methods are based on catch and effort statistics, biological information including age and reproductive status, marking and sightings records.Catch effort data have to be used with caution, because of changes in species preference, shifts in the whaling grounds and national fleet variations. With allowance made for these factors, cumulative catches adjusted for recruitment can be used to estimate the initial stock number. Changes in stock density after known catches also lead to abundance estimates. Logarithmic regression of age composition data are used to find the total mortality rates. The natural mortality can be estimated from early season catches in a fishery or pre‐fishery year classes caught more recently; fishing mortality is found by subtraction, which again leads to abundance estimates. Mathematical approaches incorporating recruitment estimates from actual age composition data and theoretical population models have been employed. Additional estimates come from mark release‐recapture experiments and direct sightings counts from whaling vessels and research ships. The latter are the only means of estimating the protected species.The yields which the various stocks can sustain are calculated from direct observations and theoretical considerations of the changes in recruitment, largely due to increased pregnancy rates and the lower ages at sexual maturity which occur in exploited stocks.The results of all the available analyses have been compared and combined to produce the population estimates and yields tabulated. The object of whale management is to bring all stocks to the levels providing the maximum or optimum sustainable yields. These are defined in terms of numbers at the moment, but may be expressed as biomass in the f