Mechanical properties, in particular, strength (tensile, shear, compressive) and porosity, are important parameters for understanding the evolution and activity of comets. However, they are notoriously difficult to measure. Unfortunately, neither Deep Impact nor other comet observations prior to Rosetta provided firm data on the strength of cometary material. This changed with the Rosetta mission and its detailed close observation data and with the landing(s) of Philae in 2014. There are already many articles and reviews in the literature that derive or compile many different strength values from various Rosetta and Philae data. In this paper, we attempt to provide an overview of the available direct and indirect data; we focus on comet Churyumov–Gerasimenko/67P but include a discussion on the Deep Impact strength results. As a prerequisite, we start by giving precise definitions of ‘strength’, discuss soil mechanics based on the Mohr–Coulomb ‘law’ of micro-gravity, and discuss bulk density and porosity, sintering, and the physics of the strength of a cohesive granular medium. We proceed by discussing the scaling of strength with the size and strain rate, which is needed to understand the observational data. We show how measured elastic properties and thermal (conductivity) data can be correlated with strength. Finally, a singular very high strength value is reviewed as well as some particularly small-strength values inferred from the bouncing motion of Philae, data from its collisions with the surface of the comet, and scratch marks it left, allegedly, on the surface close to its final resting site. The synthesis is presented as an overview figure of the tensile and compressive strength of cometary matter as a function of the size scale; conclusions about the size dependence and apparent natural variability of strength are drawn.