The eruption is being closely monitored for ash. At present time, officials do not expect a repeat of 2010, when the Eyjafjallajökull volcano grounded all flights in Europe. Aviation rules were changed after the shutdown. For example, in 2011, Iceland's Grímsvötn volcano blasted through ice in southeast Iceland (not far from Baroarbunga) and blew ash 12 miles (20 km) high, yet only 1 percent of Europe's flights were cancelled.
A more immediate threat is the glacial meltwater. Earlier this week, officials closed roads and evacuated tourists north of Baroarbunga. While the remote area is sparsely settled, the melting glacier could flood popular tourist sites and Iceland's main road.
Icelandic officials are monitoring the volcano with a dense network of earthquake sensors, radar and GPS stations. They're also watching water levels in the Jökulsá á Fjöllum river, the outlet for glacial meltwater. There are also three webcams. There are also three webcams. You can watch them here and here.