The dynamics of museum artefacts and statues under fast-dynamic excitations arising from explosions is investigated here. The study takes root in the existing knowledge and theory of inverted pendulum structures subjected to earthquake loadings and extends them to non-symmetrical pulses due to blast waves. New analytical, closed-form solutions for the rocking response are derived and the overturning domain of slender blocks is determined. The analytical findings and assumptions are validated through detailed three-dimensional numerical simulations, which consider the full interaction between the blast waves and the structure (e.g. diffraction, rarefaction, multiple reflections, no-normal incidence, uplifting etc.). We prove that unilateral rocking response and overturning are predominant mechanisms compared to sliding and up-lifting under explosive loadings. We develop design charts to be used as a straightforward decision-making tool for determining the critical stand-off distance between the explosive source and the target to prevent overturning, which can be helpful in different applications. Finally, the assessment of the minimum perimeter around museum artefacts for protection against explosions is discussed for some emblematic statues.