Nowadays, Decentralized Exchanges are a significant component of the financial world. Billions of dollars are traded daily on these venues, and the exchanged volume seems meant to increase further. A milestone in such growth is Uniswap v3. Its main feature, Concentrated Liquidity, has revolutionized the liquidity provision and how we think about it, posing new challenges and reward opportunities for Liquidity Providers. As a result, it has shortly become the most traded decentralized exchange. The industry mainly drives this innovation, and the academic research follows with several contributions mainly oriented toward optimizing profit opportunities. Nonetheless, little attention has been paid to analyzing the statistical properties of such markets and highlighting common patterns that are frequently noticed. Thus, our work aims to fill this gap. Specifically, we examine the price and liquidity time series from a microstructural point of view, starting from event-time frequency. Our study is carried out on the eighteen most active pools in Uniswap v3. The analysis is focused on detecting statistical properties such as particular effects in autocorrelation, long-memory, and dependencies between the market variables. Furthermore, we investigate the main clusters of agents entering the market and their impact. Our ultimate aim is twofold. On one side, we collect the essential features of Uniswap v3 and provide a practical guide to researchers working in this field. On the other side, we track some directions for future studies in this field.