Dominican Republic

Basics
The Dominican Republic has 4 physical network providers and run a GSM and incompatible CDMA system simultanously. Claro is market leader with the best coverage followed by Orange. Viva and Tricom have much smaller networks.
 * Claro (formerly Codetel, by América Móvil)
 * Orange (by French Telecom)
 * Viva
 * Tricom

Frequencies and compatibilities
Not only CDMA and GSM are used at the same time, but very different frequencies for GSM too by the different providers:
 * CDMA is not compatible with GSM-phones (for details see USA introduction)

To cut a long story short: If you come from a GSM-provider in the US (like AT&T or T-Mobile USA), Claro has probably the better compatibility with your device. If you carry a device from your home market in Europe or Asia, Orange will be more compatible. Anyway, you should make a network scan, before you buy a SIM card.

As Viva doesn't offer 3G data for GSM-systems and Tricom centers on Triple-Play-markets in a small area up to now, only the two major providers Claro and Orange are shown in detail.

Registration
According to a new law, all mobile phone lines must be registered by 12/6/2014. So be sure to buy your SIM in an official store (Photo ID required) or register it after buying somewhere else.

Claro (formerly Codetel)
Claro, run by Mexican tycoon Carlos Slim and it's América Móviles company, is the clear market leader in the DR. It has the best network and more than 2/3 of the national subscribers. For a rough coverage map scroll down. Claro has started with 4G/LTE recently however on the rare 1700 / AWS frequency.

Orange
Orange, run by French Telecom, has the smaller network compared to Claro, but still a good coverage in 2G and 3G countrywide. Rough coverage map. It gives better compatibility with devices from Europe, Asia or Australia (see Basics). It has started with LTE on 1800 Mhz in 2012 but is still limited to the capital area of Santo Domingo.