Ceramic aerogels are excellent ultralight-weight thermal insulators yet impractical due to their tendency towards structural degradation at elevated temperatures, under mechanical disturbances, or in humid environments. Here, we present flexible and durable alumina/zirconia fibrous aerogels (AZFA) fabricated using 3D sol–gel electrospinning — a technique enabling in situ formation of 3D fiber assemblies with significantly reduced time consumption and low processing cost compared to most existing methods. Our AZFAs exhibit ultralow density (> 3.4 mg cm−3), low thermal conductivity (> 21.6 mW m−1 K−1), excellent fire resistance, while remaining mechanically elastic and flexible at 1300 °C, and thermally stable at 1500 °C. We investigate the underlying structure-thermal conductivity relationships, demonstrating that the macroscopic fiber arrangement dictates the solid-phase thermal conduction, and the mesopores in the fiber effectively trap air thereby decreasing the gas conduction. We show experimentally and theoretically that directional heat transport, i.e., anisotropic thermal conductivity, can be achieved through compressing the fiber network. We further solve the moisture sensitivity problem of common fibrous aerogels through fluorination coating. The resulting material possesses excellent hydrophobicity and self-cleaning properties, which can provide reliable thermal insulation under various conditions, including but not limited to high-temperature conditions in vehicles and aircraft, humid conditions in buildings, and underwater environments for oil pipelines.