The energy-based Blended Quasicontinuum method (BQCE) is used to simulate defects such as cracks and vacancies in crystalline materials such as metals, graphene, and silicon. BQCE is an atomistic-to-continuum coupling. That is, BQCE uses an accurate but expensive atomistic model (molecular mechanics) near defects, and uses a less expensive continuum model (elasticity) throughout the bulk of the crystal. After a general discussion of the difficulties encountered in atomistic-to-continuum coupling, I will present a numerical analysis of BQCE. I will also discuss some novel continuum models which are motivated by the application of BQCE to materials, like silicon, with multi-lattice structure.