We introduce PyRTL, a Python embedded hardware design language that helps concisely and precisely describe digital hardware structures. Rather than attempt to infer a good design via HLS, PyRTL provides a wrapper over a well-defined "core" set of primitives in a way that empowers digital hardware design teaching and research. The proposed system takes advantage of the programming language features of Python to allow interesting design patterns to be expressed succinctly, and encourage the rapid generation of tooling and transforms over a custom intermediate representation. We describe PyRTL as a language, its core semantics, the transform generation interface, and explore its application to several different design patterns and analysis tools. Also, we demonstrate the integration of PyRTL-generated hardware overlays into Xilinx PYNQ platform. The resulting system provides an almost "pure" pythonic experience for the prototyping and evaluation of FPGA-based SoCs.