Mobile responsive design, chatbots, and Accelerated Mobile Pages (AMP) are important trends for 2020-21 website development according to the document. Responsive design makes websites accessible across devices and can increase traffic, while chatbots can boost sales and customer support. AMP pages load promptly on mobile to enhance the user experience and potentially increase sales by 20% compared to non-AMP sites. Other trends include modular design for flexibility, voice search integration, and Motion UI for emotional engagement and increased user activity.