We first consider the estimation of the finite rate of population increase or population growth rate, lambda sub i, using capture-recapture data from open populations. We review estimation and modelling of lambda sub i under three main approaches to modelling open-population data: the classic approach of Jolly (1965) and Seber (1965), the superpopulation approach of Crosbie & Manly (1985) and Schwarz & Arnason (1996), and the temporal symmetry approach of Pradel (1996). Next, we consider the contributions of different demographic components to lambda sub i using a probabilistic approach based on the composition of the population at time i + 1 (Nichols et al., 2000b). The parameters of interest are identical to the seniority parameters, gamma sub i, of Pradel (1996). We review estimation of gamma sub i under the classic, superpopulation, and temporal symmetry approaches. We then compare these direct estimation approaches for lambda sub i and gamma sub i with analogues computed using projection matrix asymptotics. We also discuss various extensions of the estimation approaches to multistate applications and to joint likelihoods involving multiple data types.