In this talk I will present some recent results regarding the complexity of parliamentary elections. I will start by presenting several well-known approaches to electing a parliament (e.g., First-Past-The-Post system, STV, division into districts) and discuss some of their potential drawbacks. Then I will describe voting rules of Monroe and Chamberlin--Courant that intuitively seem to be very appealing, but which have high computational complexity of winner determination. In the main part of the talk I will discuss some attempts at fighting with this high complexity.