I will take brittle cracks as examples to address the issues in coupled atomistic and continuum modeling, with an emphasis on differences between interface conditions for static and dynamic problems. For Static problems, the issue can be resolved by imposing consistency conditions. The necessary and sufficient condition for uniform first-order accuracy and, consequently,the elimination of the "ghost force" is formulated in terms of the reconstruction schemes. Examples of reconstruction schemes that satisfy this condition are presented. Transition between atom-based and element-based summation rules will be studied. While for dynamic cases, one has to deal with wave reflections as well. I will present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for Multiscale modeling ---the heterogeneous multiscale method (HMM). I will derive an explicit coupling condition at the atomistic/continuum interface. Application to the dynamics of brittle cracks under various loading conditions is presented as test examples.