Autobidding is revolutionizing online advertising, providing advertisers with simplified campaign management and enhanced performance through real-time optimization. This talk explores the key challenges and emerging trends in the autobidding world, together with some recent works in this area. We first delve into the design of bidding algorithms, introducing a near-optimal low-regret algorithm for autobidders with budget and ROI constraints, against the best Lipschitz function benchmark. The result applies to a wide range of auctions, most notably any mixture of first and second price auctions. Next, we study the auction design problem where autobidders compete across multiple platforms. Our findings demonstrate that first-price auctions, while optimal in isolated settings, may not maximize revenue of separate platforms in multi-platform environments.