It is a fundamental problem to calculate the homotopy groups of spaces and to understand their structures.This is equivalent to consider the homotopy groups of the loop spaces ΩnX (n≥1) of spaces X.The advantage of the latter is that ΩnX (n≥1) have rich structures which may be very helpful.In this talk,I shall explain my idea,proposed in my PhD thesis defended in June 2012,and results on uncovering the structures of homotopy groups.Roughly speaking,it is to decompose the action of little n-cubes operads (n>1) on n-fold loop spaces into many small pieces,and then use a special class of them to construct certain new operations on n-fold loop spaces.These operations can induce operations on homotopy groups which can be assembled together to give a conceptual description of the strutures of homotopy groups.