The current trend in web design is clean and minimalistic. Adobe Illustrator is vector based, perfect for drawing graphics, expermimenting with color, and web fonts. Flat design has really given Illustrator users more leverage in the web world. It is good for responsive web, workflow, and extracting CSS.
Adobe Illustrator CC does not limit you to a specific screen resolution. You can create several artboards in a file, allowing you to easily show how your webpage looks at different breakpoints. SVGs are not only vector, which is awesome for re-sizing, they tend to be small files, which is great for bandwidth.
Adobe Illustrator can help with your workflow in many ways. One is that you can create symbols, save, and use them in later projects. Another help is the new Typekit, which is connected with Ai CC so you can design directly with web fonts. Other features are the new pixel perfect envirmonment and the 9-slice scaling tool. It also allows you to easily wireframe your projects.
Ai CC now can create clean CSS files based on your Character Styles and other things, so your workload shrinks, allowing you to focus more on the HTML. For instance, my 'title' is saved as a Character Style named 'h1' with font-size 32pt, white, and bold...Illustrator will put these CSS rules together for you. All you have to do is export it!