In recent years probabilistic methods have proved useful in the solution of several difficult problems in group theory. In some cases the probabilistic nature of the problem has been apparent from its formulation, but in other cases the use of probability seems surprising, and cannot be anticipated by the nature of the problem. The roots of the subject lie in a seies of papers by Erdos and Turan in which they study the properties of random permutations, and develop a statistical theory for the symmetric group. John Dixon used the Erdos-Turan theory to settle an old conjecture that two randomly chosen elements of an alternating group of degree n will generate the whole group with probability tending to 1 as n tends to infinity. Dixon conjectured that the same result should be true for any family of finite simple groups. This was eventually proved, using much of the information on maximal subgroups discussed above. The proof of this conjecture has led to further results and problems in probabilistic group theory. One particular highlight was the well known question: which simple groups are images of the modular group PSL(2,Z) ? A necessary and sufficient condition for this is that the simple group in question be (2,3)-generated - that is, generated by an element of order 2 and an element of order 3. It was shown recently by Liebeck and Shalev that, which the exception of one 4-dimensional family, all but finitely many simple groups are (2,3)-generated; much stronger than this, randomly chosen elements of orders 2,3 will generate with probability tending to 1. Thus there are interesting results fast appearing in this area; however, the subject is really in its infancy, and there are many directions to pursue.