In plant quantitative genetic studies conducted ex situ, the large number of seeds produced per individual has promoted the use of open-pollinated progeny tests. In subsequent analyses, seeds collected on the same mother-plant are assumed to be half-sibs. The consequences of the departure from half-sib assumption in progeny tests have been investigated since the 1960s using simulation approaches and, more recently, using molecular-based experimental approaches. This review aims to synthesize the results and conclusions of these simulation and empirical studies. We focus on tree species, where controlled crosses are difficult to carry out experimentally and departures from half-sib assumptions occur frequently in natural populations. First, the average level of relatedness expected within maternal progeny for many tree populations is higher than that of half-sibs. This is the consequence of non-random mating resulting from the small number of effective pollen donors per female, unequal male reproductive success and/or selfing. As result, estimates of genetic variance and heritability for quantitative traits may be upward biased. Alternatively, inbreeding depression, dominance effects and the heterogeneity of the male gamete pool among females are often neglected, which may lead to underestimation of the heritability of traits. A correction based on the mean genetic relatedness between offspring and the relatedness between parents is often used to compensate those biases. However, such correction cannot accurately adjust the estimates in situations where variable levels of genetic relatedness among families, dominance effects or inbreeding depression exist within the progeny. An alternative and promising approach is the use of the "animal model" approach, which optimizes the use of molecular data and paternal information to estimate heritability more accurately.