Stochastic effects in biochemical systems including gene regulatory networks are commonly studied using the stochastic simulation algorithm. An alternative means of exploring stochastic dynamics is by means of approximations of the chemical master equation or the reaction-diffusion master equation. In the first part of this talk, I will present some of our recent work on deriving approximate solutions to a chemical master equation model of gene expression in mammalian cells which includes cell division, gene duplication, dosage compensation, growth-dependent transcription, mRNA maturation and translation. In the second part of the talk, I will discuss the construction of new stochastic spatial models that can approximately take into account excluded-volume interactions. The number distributions obtained from such an approach can be considerably different than those given by the conventional reaction-diffusion master equation (and the chemical master equation) thus suggesting that macromolecular crowding plays a significant role in controlling the dynamics of noisy intracellular reactions