I found a similar question here, with the answer: "you should always define the width and height in the image tag." But it is from 2009.
In the meantime, many things has changed on frontend. We are all doing responsive page design now, for many devices and sizes simultaneously (mobile, tablet, desktop...).
So, I wonder is it still necessary to specify the width and height attributes in 2016, and for what reason (for responsive, page speed, SEO...)?
img element has width and height attributes, but they're not required under any
Width and height attributes were only 'required' or relevant to reserve the space on the page and prevent the page moving around as it loads - which is important. This can be achieved using CSS instead providing the CSS loads quickly enough - it is likely to load before the images anyway, so all should be good.
It is also possible (and valid) to specify just one attribute, width or height and the browser will calculate the omitted value in order to maintain the correct aspect ratio.
You can specify percent values in the attributes if required. You don't need to use CSS for this, if that is what you are implying.
Also, it is relevant to add - Under HTML5 the width and height can only take a pixel value, in other words a valid non-negative integer.
Whether you use the width and height attributes can depend on your design. If you have lots of differently sized images, do you want to lump all the dimensions in the CSS or include them with the img?