Deep Learning Large Language Models (LLMs) have the potential to automate and simplify code writing tasks. One of the emerging applications of LLMs is hardware design, where natural language interaction can be used to generate, annotate, and correct code in a Hardware Description Language (HDL), such as Verilog. This work provides an overview of the current state of using LLMs to generate Verilog code, highlighting their capabilities, accuracy, and techniques to improve the design quality. It also reviews the existing benchmarks to evaluate the correctness and quality of generated HDL code, enabling a fair comparison of different models and strategies.