A weak solution to the Einstein equations can be defined if the metric is continuous and the derivatives of the metric are locally square integrable. In order to show that a particular solution cannot be extended as a weak solution it thus suffices to show that it is inextendible as a Lorentzian manifold in this regularity class. In this talk I will review the proof of the $C^0$-inextendibility of the maximal analytic Schwarzschild spacetime and conclude with more recent developments concerning weak null singularities.