Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of evolution in response to natural selection, are best developed for traits with normal distributions, yet many traits of evolutionary interest, such as most life history and behavioural traits, have inherently non-normal distributions. It is therefore becoming increasingly common to estimate quantitative genetic parameters, such as additive genetic variances, for non-normal traits using generalised linear mixed model (GLMM) analyses. These statistical methods provide inferences on a statistically-convenient latent scale, but not on the scale upon which traits are expressed. We provide a general approach for calculating quantitative genetic parameters on the observed scale for arbitrary GLMMs. Our approach requires no additional assumptions beyond those that made when adopting GLMM-based quantitative genetic analysis. We show that existing formulae for Binomial and Poisson distributions, in particular the threshold models for binary traits, are special cases in our framework. We use simulations to demonstrate the accuracy of our method for predicting the evolutionary response to selection and further illustrate our approach by applying it to data from a natural study population with pedigree information. Our framework is implemented in an R package, \textsc{QGglmm} (\url{https://github.com/devillemereuil/qgglmm}).