Two-dimensional conformally invariant quantum field theories (CFTs for short) form a sprawling network of ideas connecting many areas of physics and mathematics. A particularly celebrated class are the rational CFTs. These are essentially characterised by having a completely reducible representation theory and only a finite number of inequivalent irreducible representations. Rational CFTs exhibit a number of extraordinary features, foremost being the Verlinde formula which determines correlation functions from certain transformation properties of the CFTs characters. Logarithmic CFTs by contrast are almost maximally awful in that their representation theory is necessarily not completely reducible and need not have finitely many inequivalent irreducible representations. I will present recent results on such logarithmic CFTs and argue that suitable generalisations of rational features exist, at least in certain cases. So things are not as bad as one might fear.