Responsive website is a really popular solutions nowadays due to the rise of mobile devices that come in different screen dimensions. And most clients would choose responsive layout because it's an "all-in-one" solution to make sure their website is easy to read and presented well in all screen dimensions.
Making a responsive website is easy. There are tools and frameworks available. However, responsive design is not a golden bullet, like all technologies, there are problems that need to be solved, and one of the most commone problems in responsive design is the images. In responsive design, wide screen layout needs high resolution and good quality big images, and a lot of times, we simply ignore the mobile users and assume they have a high speed network on their mobile phone too. So, most of the time, even though they are using mobile, but they are still loading images assets of wide screen.
Here we have a pretty useful infographic created by awwwards.com. A quick glance at the problems, needs and solutions for responsive images. And the future solution