In natural flocks/swarms, it is very appealing that low-level individual intelligence and communication can yield advanced coordinated collective behaviors such as congregation, synchronization and migration. Firstly, we seek to understand the role of predictive mechanisms in the forming and evolving of flocks/swarms by using both numerical simulations and mathematical analyses. Secondly, by incorporating some predictive mechanism into a few pinning nodes, we show that convergence procedure to consensus can be substantially accelerated in networks of interconnected dynamic agents while physically maintaining the network topology. Such an acceleration stems from the compression mechanism of the eigenspectrum of the state matrix conferred by the predictive mechanism. Thirdly, some model predictive control protocols are developed to achieve consensus for a class of discrete-time double-integrator multi-agent systems with input constraints. Associated sufficient conditions such as that the proximity net has a directed spanning tree and that the sampling period is sufficiently small are proposed. Moreover, the control horizon is extended to larger than one, which endows sufficient degrees of freedom to accelerate the convergence to consensus.