Internet technology and website design standards have hit puberty and have finally grown out of that awkward mobile website phase. Mobile websites have matured into responsive web designs, which give websites the ability to respond to any device screen size while maintaining consistency with content and user experience. Mobile websites, although clunky and difficult to manage, still have a place on the web; but eventually will become extinct (we hope).
The mobile website world has been taken over by responsive web design. So what happened to mobile website design? It's still there and still beneficial in some cases, but for the most part mobile websites have evolved into responsive websites.
When "smart" phones were first Internet enabled, businesses realized it could be advantageous for content to be optimized for the mobile web. The only option at that time was to implement a mobile website design that coincided with businesses' primary website, but had an optimized layout for the much smaller mobile browsers. This was a great solution with many benefits, but it also had its challenges.
A new trend has taken over the mobile web. Responsive web design has been a game changer in mobile website design, and website design in general. Responsive web design has become a best practice because it addresses all the challenges introduced by mobile websites.
For a time, you were not important if you did not have a mobile app. While a mobile app has many benefits and can be used effectively, please do not think people are going to download an app to read your website. Build a responsive website to reach your audience and you might also be pleasantly surprised at the native functions HTML5 provides, if needed.