Here is for the nostalgic of Radio Buttons, Ali Najafizadeh has brought them back with its new component.

react-native-radio-button-classic on GitHub (Example)

<Radio
  onSelect={this.onSelect.bind(this)}
  defaultSelect={this.state.optionSelected - 1}
>
  <Option color="gray" selectedColor="#008BEF">
    <Item title="First Options" description="This is your First Option" />
  </Option>
  <Option color="gray" selectedColor="#008BEF">
    <Item title="Second Options" description="This is your Second Option" />
  </Option>
  <Option color="gray" selectedColor="#008BEF">
    <Item title="Third Options" description="This is your thrid Option" />
  </Option>
</Radio>