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Carbon aerogels are elastic, mechanically robust and fatigue resistant and are known for their promising applications in the fields of soft robotics, pressure sensors etc. However, these aerogels are generally fragile and/or easily deformable, which limits their applications. Here, we report a synthesis strategy for fabricating highly compressible and fatigue-resistant aerogels by assembling interconnected carbon tubes. The carbon tube aerogels demonstrate near-zero Poisson’s ratio, exhibit a maximum strength of more than 20 MPa and a completely recoverable strain up to 99%. They show high fatigue resistance (less than 1.5% permanent degradation after 1,000 cycles at 99% strain) and are thermally stable up to 2,500 °C in an Ar atmosphere. Additionally, they possess tunable conductivity and electromagnetic shielding. The combined mechanical and multi-functional properties offer an attractive material for the use in harsh environments.