In this talk, I will present two thermodynamically consistent phase-field models for simulating motion and shape transformation of vesicles under flow conditions. In details, I will also describe a general slip boundary condition for the interaction between vesicles and the wall of the fluid domain, and a generalized multi-dimensional Lennard-Jones potential to account for short-range repulsion and adhesive bonding between cells. Second-order accurate in both space and time C^0 finite element method is developed to solve the model governing equations. Various numerical tests confirm the convergence, energy stability, and conservation of mass and surface area of cells of the proposed scheme. Vesicles with different mechanical properties are also used to explain the pathological risk for patients with sickle cell disease.