The idea of solving computational problems the way Nature solves its problems is nothing new. Evolutionary paradigms have been borrowed from biology, neurological paradigms from cognitive sciences and thermodynamic and quantum paradigms from physics, just to name a few. Common to these examples is the adaptive and distributed approach to problem solving, in contrast to the straight-forward logic of classical computation. However, none of the Nature's inspired paradigms have so far managed to go beyond the limits of classical Turing machines, despite the fact that several of these natural computation substrates are in principle capable to overcoming those limits. In this talk is defended the position of Thermodynamic Computing (TC) as a promising approach with even greater potential and lower hardware costs than Quantum Computing (QC).