Embedding widgets in a DOM that you don't own can be frustrating due to style collisions, and traditional solutions like iFrames have limitations such as size issues, communication problems, and inability to customize styles. A more modern approach is to use the Shadow DOM, an API for DOM encapsulation that allows creating a hidden DOM tree attached to elements in the regular DOM tree, enabling isolation of styles and improving composite user interfaces. The Shadow DOM can be used with CSS specificity, React, or other libraries, making it easier to create beautiful and customizable user experiences without the need for iFrames or explicit CSS tweaking.