A quarter of a century ago, Eva Jablonka and Marion J Lamb put forward a model (reprinted in this issue of IJE) to explain how the functional history of a gene might influence its expression in subsequent generations. They were particularly interested in the idea that an environmental stimulus acting on the parent could alter the behaviour of a gene in the offspring. The model is simple and is depicted in Figure 1. The environment stimulates a change in transcription that is associated with chemical modifications to the DNA or to the proteins that package the DNA.These modifications are inherited via the germ line and influence transcriptional activity in the next generation. In other words, epigenetic marks, generally considered to be cleared between generations, are retained at some loci and convey a memory of the altered activity state to the offspring. This model emerged in conjunction with the developing interest among biologists in epigenetics, in particular the finding that demethylation of DNA could result in gene activation and that, at least in cell culture, the addition of an environmental stimulus, 5-azacytidine, could change the level of DNA methylation. Patterns of DNA methylation had already been shown to be mitotically heritable in vitro. At the same time, observations that the expression of some autosomal genes is dependent on the sex of the parent from which they are inherited, termed genomic imprinting, were being made. The latter requires that ‘epigenetic marks’ be inherited across meiosis to enable the zygote (fertilized egg) to discriminate between the paternal and maternal alleles. From these and other findings, Eva Jablonka and Marion J Lamb speculated on the existence of a form of ‘Lamarckian’ inheritance that involved an adaptive response to the environment based on epigenetic variations. This bold hypothesis has generated a great deal of interest and has driven experiments in the field for the last couple of decades. Here we review the current evidence for and against the inheritance of acquired characteristics. Does it ever happen?