This talk describes the evolution of studies of chaos in Yang-Mills fields, gravity, and cosmology. The main subject is a BKL regime near the singularity t = 0 and its survival in higher dimensions and in string theory. We also describe the recent progress in the search for particle-like solutions of the Einstein-Yang-Mills system (monopoles and dyons), colored black holes and the problem of their stability. I. INTRODUCTION The great achievements of theoretical physics in the 20th century,

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... ein's theory of general relativity and the Yang-Mills theory of non-Abelian gauge fields, have many common properties: both are gauge theories and they are, in contrast to Maxwell's theory of the electromagnetic field, nonlinear. From this point of view, the chaoticity of the corresponding fields is not a surprise. On the other hand, there are many examples of stable solutions (solitons) of nonlinear field equations. Thus, the question of chaos in the equations of general relativity (GR) and the Yang-Mills (YM) equations is not a trivial and straightforward one. The evolution of our insight into chaos in the YM theory provides a good illustration for this nontriviality.