This article describes briefly and simply the theory of random walks and some of the important issues it raises concerning the work of market analysts. A discussion of two common approaches to predicting stock prices—the chartist (or technical) theories and the theory of fundamental (or intrinsic) value—allows the reader to put the theory of random walks into perspective. The theory of the market as efficient (at least semistrong efficient) and characterized as a random walk states that successive price changes in individual securities are independent and a series of stock price changes has no memory; thus, the past history of the series cannot be used to predict the future history. Empirical evidence indicates that, although price changes may not be strictly independent, the dependence is so slight that a simple buy-and-hold strategy beats any strategy based on mechanical trading rules. The implications of the market being a random walk are devastating for chartism. For fundamental value analysis, the implications are more complex. If the market is efficient, stock prices at any point in time represent good estimates of intrinsic value, so additional analysis is useless unless the analyst has new (private) information or insights. The challenge for each type of analysis is to show that their methods produce more return than a random sample of securities.