Time dependent problems are often solved using time marching schemes. Such schemes are inherently sequential in nature, and at first sight it does not seem to be possible to work on more than one time step simultaneously. I first present several classical attempts to obtain time parallelism, including unsuccessful ones, and then show a new approach introduced in 2001 by Lions, Maday and Turinici called the parareal algorithm. I will interpreted this new algorithm in the framework of classical time parallel algorithms, present a convergence analysis, and illustrate the results with numerical experiments, which indicate that indeed for certain problems, time parallel computations are a viable strategy.