Arising technologies related to vehicle-to-vehicle (V2V) communication can significantly improve the safety and efficiency of connected vehicle systems. This allows cars to obtain detailed information about the motion of distant vehicles and such information can be presented to the driver or incorporated in advanced vehicle control systems. However, when designing such controllers, one faces many fundamental challenges: (i) the controllers must function in heterogeneous traffic environment that include conventional vehicles; (ii) high level of modularity is required which allow the formation and disband of ad-hoc convoys; (iii) the system must be robust against delays the communication channels that arise due to intermittencies and packet drops. In this talk I discuss some novel mathematical techniques that allow us to target these challenges systematically. Our results allow one to redesign the longitudinal dynamics of heterogeneous multi-vehicle systems by exploiting connectivity.