Apple’s look-and-feel style was dominating in mobile and even web design for a long time. Inspired by Steve Jobs the iOS UI/UX was treated as almost absolute standard. Even some of Android developers and designers were trying to copy iOS practices in their projects. Keep in mind, you should have very important reason to fight a framework. Recently, Google, as main supporter of Android platform, announced Material Design [http://www.google.com/design/spec/material-design/introduction.html] their point of view on both questions Usability and UI design. Besides, Material Design is not just pure theoretical specification. There is new Android 5.0 “Lollipop” version available. It’s based on Material Design. So, you are able to try it live, as well.
Flat, non flat and material
About 10 years ago the web design was pretty huge visually. It had a lot of almost realistic graphics with 3D effects, shadows, gradients, etc. Even small buttons and icons were 3D-like. Later, the web became more productive and useful. For now, it’s not just pure visual set of pages to represent some information. It’s rather applications with thick UI.