Programming abstractions decrease the cognitive gap between program idealization and expression. In the software domain, this high-level expressive power is achieved through layered abstractions - virtual machines, compilers, operating systems - which translate, at design and runtime, programmer visible code into hardware-compatible code. While this paradigm is ideal for static, i.e., unmodifiable, hardware, several of these abstractions break down when programming configurable hardware. State of the art hardware/software co-design techniques (e.g., High Level Synthesis (HLS), Intermediate Fabrics) are, for the most part, ad hoc patches to the traditional abstraction stack, applicable only to specific toolchains or software components. In this paper, we survey current hardware design and hardware/software co-design abstractions, from the perspective of the design language/toolchain. We perform a systematic analysis of different design paradigms, including HLS, Domain Specific Languages (DSL), and new-generation Hardware Description Languages (HDL). We analyze how these paradigms differ in expressiveness, support for hardware/software interaction, hierarchy and modularity, HDL interoperability, and interface with the outside world.