This paper reviews the use of Convolutional Neural Networks (CNNs) and Verilog in recognizing handwritten numbers, a key task in image processing and pattern recognition. Handwritten number recognition is important for various applications like sorting mail and processing bank checks. CNNs have greatly improved this field by offering effective and accurate recognition methods. We explore different CNN methods and designs used for this task, discussing how these networks have evolved and their main features and limitations. We also look at how Verilog, a language for describing hardware, is used to implement these networks on devices like Field-Programmable Gate Arrays (FPGAs). Combining CNNs with FPGA implementations in Verilog is promising for creating fast, energy-efficient and real-time recognition systems. The paper reviews important studies in this part, comparing their approaches and results. We discuss challenges like managing resources, saving power, and maintaining accuracy within hardware limits. Lastly, we suggest future research directions, focusing on making these systems more efficient and adaptable for practical use.