Randomness is essential for understanding our physical world and is ubiquitous in our daily life. Randomness also plays a crucial role in algorithms research. In this talk, I will present a number of examples for the use of randomness in the design and analysis of algorithms. We start with the simulation of physical growth processes and random walks. Further examples will be discrete optimization, high-dimensional volume computation and distributed computing. The key ingredient will be the appropriate use of randomness. I will give several examples where the right dose of randomness makes algorithms both simpler and faster.