In this thesis, we study the Cucker-Smale model which describes the flocking phenomena. In the Cucker-Smale model, the dynamics of the particles are presented by the couplings proportional to the relative velocities between each pair of particles. We focus on the sufficient conditions to achieve the local flocking phenomena in various scenarios using Lyapunov functional approach while the sufficient condition to the global flocking was suggested by Cucker and Smale. We also consider the hydrodynamic model of Cucker-Smale particles, which is the macroscopic description through the mean-field limit process. We avoid free boundary problems by describing Lagrangian variables.