The interconnection of molecular machines with different functionalities to form molecular communication systems can increase the number of design possibilities and overcome the limited reliability of the individual molecular machines. Artificial information exchange using molecular signals would also expand the capabilities of single engineered cell populations by providing them a way to cooperate across heterogeneous cell populations for the applications of synthetic biology and lab-on-a-chip systems. The realization of molecular communication systems necessitates analysis and design of the communication channel, where the information carrying molecular signal is transported from the transmitter to the receiver. In this thesis, significant progress towards the use of microfluidic channels to interconnect molecular transmitter and receiver pairs is presented. System-theoretic analysis of the microfluidic channels are performed, and a finite-impulse response filter is designed using microfluidic channels. The spectral density of the propagation noise is studied and the additive white Gaussian noise channel model is developed. Memory due to inter-diffusion of the transmitted molecular signals is also modeled. Furthermore, the interference modeling is performed for multiple transmitters and its impact on the communication capacity is shown. Finally, the efficient sampling of the signal transduction by engineered bacterial receivers connected to a microfluidic channel is investigated for the detection of the pulse-amplitude modulated molecular signals. This work lays the foundation for molecular communication over microfluidic channels that will enable interconnection of engineered molecular machines.