String duality
Unfortunately, until recently, the formulation of string theory was necessarily only perturbative in nature where the Feynman diagrams correspond to surfaces. As is also the case for many quantum field theories, this perturbation expansion is only asymptotic, so that the theory was at best incomplete. There is also no a priori reason to assume that the string coupling constant, which controls the expansion in terms of surfaces, is small. Furthermore, there seemed to be five independent perturbative string theories, that differed dramatically in their basic properties, such as world-sheet geometry, gauge groups and supersymmetries.
However, in the last two years we have witnessed dramatic developments bringing for the first time nonperturbative questions into reach. In a confluence of a wide variety of ideas involving supersymmetry, solitons and nonlinear symmetries, many of them dating back to the 70s and 80s, the structure, internal consistency and beauty of string theory has greatly improved. We have now a much better and clearer picture what the theory is about.
Crucial in all this has been the concept of string duality. In fact, duality has been a powerful idea in physics for a long time, both in statistical mechanics and field theory. The transformation to a dual set of variables can translate a difficult question (such as strong-coupling behaviour) into a much more accessible one (weak-coupling behaviour). String duality is the statement that all five diffferent perturbative strings are related in such a fashion and are just expansions of one single unified theory around different backgrounds. In many respects duality can be used as an organizing principle. In a collective effort during the last two years a mass of evidence for these proposed dualities has been found. In particular the so-called S-dualities that relate strong and weak couplings, can be used to probe the nature of quantum gravity at strong coupling, a unicum in history.
D-branes
One of the consequences of all this has been the realisation that string theory does not only includes strings but also various higher dimensional objects, known as branes. After compactification these solitonic objects can be thought of as black holes in the four-dimensional world. In particular the description of these branes as exact string solitons in the form of D-branes by Polchinski has been one of the most important developments.
The D-brane is simply a place in space-time where the string can begin or end. The resulting open strings lead to world-volume theories for these D-branes that involve nonabelian gauge theories. This allows us to translate actual nonperturbative computations, such as the determination of soliton spectra, into the language of the dynamics of nonabelian gauge theories. Vice versa string theory can be used to derive new exact results in (supersymmetric) gauge theories, such as the mysterious dualities of Seiberg. It also has brought us a dramatically different outlook on the space-time singularities, where on short distances the space-time coordinates become non-commuting matrices.
M-theory, matrix models and fivebranes
At this moment there are many open questions. Particularly important is the determination of the correct degrees of freedom that can give an ultimate fundamental, nonperturbative description of string theory. It is clear that such a formulation will go beyond strings, that only capture the perturbative physics. It should make the large hidden quantum symmetry groups (U-duality groups) more manifest.
A good starting point for such an approach is the eleven-dimensional formulation, so-called M-theory. M-theory should reduce to eleven-dimensional supergravity in weak coupling and reduce upon compactification of one dimension to the ten-dimensional type IIA superstring. Recently, there have been more concrete proposal that M-theory should be formulated as a matrix model, incorporating the non-commutativity and the relation with nonabelian gauge theory dynamics from the start. At present this is one of the main themes in research.