The moment problem is an important class of inverse problems that naturally appear in many areas of science and mathematics. In the study of moment problems, traditional tools and techniques have been used from a variety of subjects, including real and complex analysis, algebraic geometry, analytic function theory, operator theory, and the extension theory for positive linear functionals on convex cones in function spaces. We can easily find that the importance of moment problem extends to various topics; in this talk we briefly look over connections between moment problems and the following:

(i) Interpolation and pencil problem

(ii) Representation of the general Fibonacci sequence

(iii) Invariant subspace problem

(iv) Subnormal completion problem

(v) Image reconstruction.