The flexslider module mentioned above seems great with it's mobile swipe support, but only images are supported and I needed videos slideshow, with overlays support. So I've added the following lines in my theme's CSS file and it worked:
.views_slideshow_cycle_main { width: 100%; }
.views_slideshow_cycle_main .views-slideshow-cycle-main-frame { width: 100% !important; height: auto; }
.views_slideshow_cycle_main .views-slideshow-cycle-main-frame-row { width: 100% !important; height: auto; }
.views_slideshow_cycle_main .field-content { max-width: 100%; width: 100%; }
.views_slideshow_cycle_main .field-content img { max-width: 100%; width: 100%; height: auto; margin: 0; padding: 0; }
With SCSS, it may be easily written as:
.views_slideshow_cycle_main {
width: 100%;
.views-slideshow-cycle-main-frame {width: 100% !important; height: auto;}
.views-slideshow-cycle-main-frame-row {width: 100% !important; height: auto;}
.field-content { max-width: 100%; width: 100%;}
.field-content img { max-width: 100%; width: 100%; height: auto; margin: 0; padding:0;}
}
The overlays were added by views_slideshow_xtra_overlay.
Adapted from This discussion