We create the above-mentioned semicircle based on a circle element:

<svg
  version="1.1"
  xmlns="http://www.w3.org/2000/svg"
  xmlns:xlink="http://www.w3.org/1999/xlink">
  <defs>
    <clipPath id="cut-off-bottom">
      <rect x="0" y="0" width="200" height="100" />
    </clipPath>
  </defs>

  <circle cx="100" cy="100" r="100" clip-path="url(#cut-off-bottom)" />
</svg>

Centered at (100,100), a circle with radius 100 is painted. The attribute clip-path references a <clipPath> element with a single rect element. This rectangular on its own would paint the upper half of the canvas black. Note, that the clipPath element is usually placed in a defs section.

The rect will not be painted, however. Instead, its pixel data will be used to determine which pixels of the circle "make it" to the final rendering. Since the rectangle covers only the upper half of the circle, the lower half of the circle will vanish:

We now have a semicircle without having to deal with arcs in path elements. For the clipping, every path inside the clipPath is inspected and evaluated together with its stroke properties and transformation. Then every part of the target lying in a transparent area of the resulting clipPath's content will not be rendered. Color, opacity, and such have no effect as long as they don't let parts vanish completely.

The effect of masking is most impressively presented with a gradient. If you want an element to fade out, you can achieve this effect quite quickly with masks.

<svg
  width="200"
  height="200"
  version="1.1"
  xmlns="http://www.w3.org/2000/svg"
  xmlns:xlink="http://www.w3.org/1999/xlink">
  <defs>
    <linearGradient id="Gradient">
      <stop offset="0" stop-color="black" />
      <stop offset="1" stop-color="white" />
    </linearGradient>
    <mask id="Mask">
      <rect x="0" y="0" width="200" height="200" fill="url(#Gradient)" />
    </mask>
  </defs>

  <rect x="0" y="0" width="200" height="200" fill="green" />
  <rect x="0" y="0" width="200" height="200" fill="red" mask="url(#Mask)" />
</svg>

You see a green-filled rect at the lowest layer and on top a red-filled rect. The latter has the mask attribute pointing to the mask element. The content of the mask is a single rect element, which is filled with a black-to-white gradient. As a result, the pixels of the red rectangle use the luminance value of the mask content as the alpha value (the transparency), and we see a green-to-red gradient as a result:

The opacity attribute lets you set the transparency for a whole element:

<rect x="0" y="0" width="100" height="100" opacity=".5" />

The above rectangle will be painted half-transparent. For the fill and stroke, there are two separate attributes, fill-opacity and stroke-opacity, that control each of those property opacities separately. Note, that the stroke will be painted on top of the filling. Hence, if you set a stroke opacity on an element, which also has a fill, the fill will shine through on half of the stroke while on the other half, the background will appear:

<svg
  width="200"
  height="200"
  version="1.1"
  xmlns="http://www.w3.org/2000/svg"
  xmlns:xlink="http://www.w3.org/1999/xlink">
  <rect x="0" y="0" width="200" height="200" fill="blue" />
  <circle
    cx="100"
    cy="100"
    r="50"
    stroke="yellow"
    stroke-width="40"
    stroke-opacity=".5"
    fill="red" />
</svg>

You see in this example the red circle on blue background. The yellow stroke is set to 50% opacity, which leads effectively to a double-color stroke.

One of the most powerful tools in a web developer's toolbox is display: none. It is therefore not a surprise that it was decided to take this CSS property into SVG as well, together with visibility and clip as defined by CSS 2. For reverting a previously set display: none, it is important to know that the initial value for all SVG elements is inline.