There are several variations of dive computer, console mounted, wrist mounted, ACW advanced computer watch (essentially a normal watch sized dive computer) or even incorporated within a mask with a heads up display (which is rather futuristically is projected onto the mask lens). In the UK console mounted dive computers are not so popular, although in most countries are by far the most popular configuration. There is no good reason why hose integrate console mounted dive computers are not more popular.
In recent years wireless integrated scuba computers have become more common, they send tank pressure data wirelessly to your computer. The great advantage of having air data is your computer can calculate your breathing rate, so it can monitor how long your air will last but also how hard you are breathing so can adjust your bottom time based on your nitrogen loading.
Thanks to miniaturisation in recent years you can now purchase a dive computer the size of a medium to large watch. These allow you to wear it both during the dive and afterwards into the evening. This has the advantage that you are unlikely to lose it. There is a downside to this, if your eyesight is not as good as it once was you may struggle to read the display.
Here in the UK wrist mounted dive computers are by far the most popular configuration. They offer a larger display, audible alarms and in most cases have the option to be air integrated.
Apart from the very entry level diving computers most have the option to interface with your PC so you can record your dives and profiles to your computer.
A more basic version of a dive computer is the bottom timer which accurately records time and depth but does not calculate no decompression times. Generally it is accepted that digital dive instruments are accurate within 1% whereas an analogue instrument would be plus or minus 10%.