A Cellular Neural Network (CNN) is a powerful processor that can significantly improve the performance of spatiotemporal applications such as pattern recognition, image processing, motion detection, when compared to the more traditional von Neumann architecture. In this paper, we show how tunneling field effect transistors (TFETs) can be utilized to enhance the performance of CNNs. Specifically, power consumption of TFET-based CNNs can be significantly lower when compared to MOSFET-based CNNs due to improved voltage controlled current sources (VCCSs) -an important component in CNN systems. We demonstrate that CNNs can benefit from low power conventional linear VCCSs implemented via TFETs. We also show that TFETs can be useful to realize non-linear VCCSs, which are either not possible or exhibit degraded performance when implemented via CMOS. Such non-linear VCCSs help to improve the performance of certain CNN operations (e.g., global maximum/minimum). We provide two case studiesimage contrast enhancement and maximum row selectionthat illustrate the benefits of non-linear VCCSs (e.g., reduced computation time, energy dissipation, etc.) when compared to CMOS-based approaches.