This paper reviews recent literature results on the mechanics of structures formed by layers of pentamode lattices alternating with stiffening plates, which can be effectively employed for the development of seismic isolation devices and vibration attenuation tools, with nearly complete band gaps for shear waves. It is shown that such structures, named pentamode bearings, can respond either in the stretching-dominated regime, or in the bending-dominated regime, depending on the nature of the joints connecting the different members. Their response is characterized by high vertical stiffness and theoretically zero shear stiffness in the stretching dominated regime, or considerably low values of such a quantity in the bending dominated regime. Available results on the experimental response of 3d printed models to combined compression and shear loading highlight that the examined structures are able to exhibit energy dissipation capacity and effective damping that are suitable for seismic isolation devices. Their fabrication does not necessarily require heavy industry, and expensive materials, being possible with ordinary 3-D printers.