Recently, there have been numerous results on the structure of sum-free sets in various settings and of solution-free sets of linear equations (arithmetic progression-free sets, for example). There is recent work by B. Green, I. Ruzsa, V. Lev, T. Luczak, T. Schoen, among others. For example, Ben Green has just solved the long-standing Cameron-Erdos conjecture. This talk will survey these results in connection with the general theory of Ruzsa on solving linear equations in integers, as well as with Ramsey theory.