FPGA-based neuromorphic architectures pose a promising viewpoint on the future of computing, but the efforts in this domain are disorganized, without a clear classification scheme for implemented structures. This results in the lack of consensus on what is important for specific groups of neuromorphic systems, e.g., based on the platform they are implemented on or the intended use case. Here, we review the approach to implementing such architectures on FPGAs over the last 25 years. We propose a new taxonomy for those systems that could help the researchers better understand the closest environment their designs reside in and devise new metrics that could fairly grade them against the other ideas.