Several issues connected with bridging methods for atomistic-to-continuum (AtC) coupling are examined. Different coupling approaches using various energy blending models are studied as well as the influence that model parameters, blending functions, and grids have on simulation results. We use the Lagrange multiplier method for enforcing constraints on the atomistic and continuum displacements in the bridge region. We also show that continuum models are not appropriate for dealing with problems with singular loads, whereas AtC bridging methods yield correct results, thus justifying the need for a multiscale method. We investigate models that involve multiple-neighbor interactions in the atomistic region, particularly focusing on a comparison of several approaches for dealing with Dirichlet boundary conditions.