Quantum mechanics is a probabilistic theory, predicting phenomena for a large number of identical systems - or the outcome of a large number of identically applied measurements. Is it thus a theory that applies only to ensembles of quantum systems, unable to address the state or dynamics of single systems? One of the fathers of the theory, Erwin Schrdinger, doubted that one would ever observe single quantum systems such as atoms or molecules. Now such observations are basic tools for fundamental and applied research alike, and they encompass even photons, the quanta of light. In 2012 such pioneering work for atoms and photons was honoured with the Nobel Prize in Physics. I shall present examples of such observations and discuss their impact on our understanding of quantum mechanics and its random nature. One of the crucial aspects is looking how the environment of a quantum system and the subsequent decoherence phenomena connects the randomness in quantum mechanics to the randomness in classical world.