Plant synthetic biology is a rapidly emerging field that aims to engineer genetic circuits to function in plants with the same reliability and precision as electronic circuits. These circuits can be used to program predictable plant behavior, producing novel traits to improve crop plant productivity, enable biosensors, and serve as platforms to synthesize chemicals and complex biomolecules. Herein we introduce the importance of developing orthogonal plant parts and the need for quantitative part characterization for mathematical modeling of complex circuits. In particular, transfer functions are important when designing electronic-like genetic controls such as toggle switches, positive/negative feedback loops, and Boolean logic gates. We then discuss potential constraints and challenges in synthetic regulatory circuit design and integration when using plants. Finally, we highlight current and potential plant synthetic regulatory circuit applications.