This article reviews numerical simulations of red blood cells (RBCs) mainly using the lattice Boltzmann method (LBM), focusing on the 2-dimensional deformation and aggregation of the cells in simple shear flow. We outline the incorporation of the immersed boundary method into the LBM, in which the membrane forces are obtained from the membrane model. The RBCs are simulated as a single biconcave capsule and as a doublet of biconcave capsules. The transition from swinging to tumbling motions of the RBCs, as induced by reducing the shear rate or increasing the membrane bending stiffness, is discussed. Also discussed is the aggregation tendency of the doublet of RBCs, for which homogenous deformability maintained RBC aggregation, whereas an increased deformability difference resulted in RBC dissociation.