How can I display just a portion of an image in HTML/CSS?

Let's say I want a way to display just the the center 50x50px of an image that's 250x250px in HTML. How can I do that. Also, is there a way to do this for css:url() references?

I'm aware of clip in CSS, but that seems to only work when used with absolute positioning.

As mentioned in the question, there is the clip css property, although it does require that the element being clipped is position: absolute; (which is a shame):

.container {
  position: relative;
}
#clip {
  position: absolute;
  clip: rect(0, 100px, 200px, 0);
  /* clip: shape(top, right, bottom, left); NB 'rect' is the only available option */
}

<div class="container">
  <img src="http://lorempixel.com/200/200/nightlife/3" />
</div>
<div class="container">
  <img id="clip" src="http://lorempixel.com/200/200/nightlife/3" />
</div>

JS Fiddle demo, for experimentation.

To supplement the original answer – somewhat belatedly – I'm editing to show the use of clip-path, which has replaced the now-deprecated clip property.

The clip-path property allows a range of options (more-so than the original clip), of:

• inset — rectangular/cuboid shapes, defined with four values as 'distance-from' (top right bottom left).
• circle — circle(diameter at x-coordinate y-coordinate).
• ellipse — ellipse(x-axis-length y-axis-length at x-coordinate y-coordinate).
• polygon — defined by a series of x/y coordinates in relation to the element's origin of the top-left corner. As the path is closed automatically the realistic minimum number of points for a polygon should be three, any fewer (two) is a line or (one) is a point: polygon(x-coordinate1 y-coordinate1, x-coordinate2 y-coordinate2, x-coordinate3 y-coordinate3, [etc...]).
• url — this can be either a local URL (using a CSS id-selector) or the URL of an external file (using a file-path) to identify an SVG, though I've not experimented with either (as yet), so I can offer no insight as to their benefit or caveat.

div.container {
  display: inline-block;
}
#rectangular {
  -webkit-clip-path: inset(30px 10px 30px 10px);
  clip-path: inset(30px 10px 30px 10px);
}
#circle {
  -webkit-clip-path: circle(75px at 50% 50%);
  clip-path: circle(75px at 50% 50%)
}
#ellipse {
  -webkit-clip-path: ellipse(75px 50px at 50% 50%);
  clip-path: ellipse(75px 50px at 50% 50%);
}
#polygon {
  -webkit-clip-path: polygon(50% 0, 100% 38%, 81% 100%, 19% 100%, 0 38%);
  clip-path: polygon(50% 0, 100% 38%, 81% 100%, 19% 100%, 0 38%);
}

<div class="container">
  <img id="control" src="http://lorempixel.com/150/150/people/1" />
</div>
<div class="container">
  <img id="rectangular" src="http://lorempixel.com/150/150/people/1" />
</div>
<div class="container">
  <img id="circle" src="http://lorempixel.com/150/150/people/1" />
</div>
<div class="container">
  <img id="ellipse" src="http://lorempixel.com/150/150/people/1" />
</div>
<div class="container">
  <img id="polygon" src="http://lorempixel.com/150/150/people/1" />
</div>

JS Fiddle demo, for experimentation.

References:

• clip — note: deprecated.
• clip-path (MDN).
• clip-path (W3C).

One way to do it is to set the image you want to display as a background in a container (td, div, span etc) and then adjust background-position to get the sprite you want.

Another alternative is the following, although not the cleanest as it assumes the image to be the only element in a container, such as in this case:

<header class="siteHeader">
  <img src="img" class="siteLogo" />
</header>

You can then use the container as a mask with the desired size, and surround the image with a negative margin to move it into the right position:

.siteHeader{
    width: 50px;
    height: 50px;
    overflow: hidden;
}

.siteHeader .siteLogo{
    margin: -100px;
}

Demo can be seen in this JSFiddle.

Only seems to work in IE>9, and probably all significant versions of all other browsers.

Adjust the background-position to move background images in different positions of the div:

div { 
  background-image: url('image url');
  background-position: 0 -250px; 
}