Many problems of fundamental and practical importance contain multiple scale solutions. Composite materials, flow and transport in porous media, and turbulent flow are examples of this type. Direct numerical simulations of these multiscale problems are extremely difficult due to the range of length scales in the underlying physical problems. In this talk, I will give an overview of the multiscale finite element method and describe some of its applications, including composite materials, wave propagation in random media, convection enhanced diffusion, flow and transport in heterogeneous porous media. It is important to point out that the multiscale finite element method is designed for problems with many or continuous spectrum of scales without scale separation. Further, we introduce a new multiscale analysis for convection dominated 3-D incompressible flow with multiscale solutions. The main idea is to construct semi-analytic multiscale solutions locally in space and time, and use them to construct the coarse grid approximation to the global multiscale solution. Our multiscale analysis provides an important guideline in designing a systematic multiscale method for computing incompressible flow with multiscale solutions.