he stochasticity of gene expression presents significant challenges to the modeling of genetic networks. A two-state model describing promoter switching, transcription and mRNA decay is the standard model of stochastic mRNA dynamics in eukaryotic cells. Here I will summarise our recent efforts to extend this model to include various biochemical/biophysical processes including mRNA maturation, partitioning of cell contents at cell division, cell cycle length variability, gene replication, dosage compensation, growth-dependent transcription and auto-regulatory feedback. I will show how despite the complexity of these processes, by making careful assumptions, it is possible to construct and solve Markov models describing the non-equilibrium dynamics of gene products in single cells. The theory is used to show that: (i) for many genes, the mRNA number distribution can be well approximated by a negative binomial distribution (with parameters that are a function of the cell age) whereas the protein number distribution is better approximated by a sum of N negative binomial distributions where the integer N is determined by the inherent stochasticity of the cell cycle length; (ii) the distributions can be considerably different for single lineage and population snapshot settings, thus highlighting a violation of the ergodic hypothesis for growing cell populations; (iii) mRNA degradation and gene activation rates are typically the most sensitive parameters for controlling mRNA noise; (iv) for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements. Our theory enable us to study how complex biological processes contribute to the fluctuations of gene products in eukaryotic cells, as well as potentially allowing a detailed quantitative comparison with experimental data via maximum likelihood methods.