stainable exploitation of marine populations is a challenging task relying on information about their current and past abundance. Fisheries‐related data can be scarce and unreliable making them unsuitable for quantitative modelling. One fishery independent method that has attracted attention in this context consists in estimating the effective population size (Ne), a concept founded in population genetics. We reviewed recent empirical studies on Ne and carried out a simulation study to evaluate the feasibility of estimating Ne in large fish populations with the currently available methods. The detailed review of 26 studies found that published empirical Ne values were very similar despite differences in species and total population sizes (N). Genetic simulations for an age‐structured fish population were carried out for a range of population and samples sizes, and Ne was estimated using the Linkage Disequilibrium method. The results showed that already for medium‐sized populations (1 million individuals) and common sample sizes (50 individuals), negative estimates were likely to occur which for real applications is commonly interpreted as indicating very large (infinite) Ne. Moreover, on average, Ne estimates were negatively biased. The simulations further indicated that around 1% of the total number of individuals might have to be sampled to ensure sufficiently precise estimates of Ne. For large marine populations, this implies rather large samples (several thousands to millions of individuals). If however such large samples were to be collected, many more population parameters than only Ne could be estimated.