Microtubules are self-assembling biological nanotubes that are essential for cell motility, cell division and intracellular trafficking. Microtubules have outstanding mechanical properties, combining high resilience and stiffness. Such a combination allows microtubules to accomplish multiple cellular functions and makes them interesting for material sciences. We review recent experiments that elucidate the relationship between molecular architecture and mechanics in microtubules and examine analogies and differences between microtubules and carbon nanotubes, which are their closest equivalent in nanotechnology. We suggest that a long-term goal in bionanotechnology should be mimicking the properties of microtubules and microtubule bundles to produce new functional nanomaterials.