The notion of “analog computing” sounds pretty dated (and might better be called natural of physical computing) but holds great promise for high-speed and high-efficiency computing in the 21st century. This talk gives a short historic overview of the development of analog (and hybrid) computers before detailing on modern developments such as automatically reconfigurable analog computers, their implementation, their applications, and the software stack required to integrated them seamlessly as co-processors with modern digital computer systems. Applications shown range from research in the field of dynamical systems to aerospace applications, industrial control systems, medical implants, artificial intelligence, etc. It will be shown that classic digital computers are about to hit fundamental boundaries, thus requiring different computational paradigms of which one of the most promising is that of analog computing. Analog computers excel in problems involving complex networks of coupled nodes such as neural networks consisting of spiking and bursting neurons, metric networks in the live sciences, etc., since they exhibit a basically constant runtime complexity of O(1).