The tubular two main advantages over the clincher:
Tubular allow a much lighter rim.
Tubular can be far more resistant to puncture than clinchers. Pinch flats, where the tube gets caught between the rim and the tire bead, are non-existent, because the tube is completely surrounded by the tubular tire casing.
What about tubeless?
Tubeless clinchers have become increasingly popular in mountain biking. Tubeless tires eliminate pinch flats and allow low tire pressure for better grip on wet, loose, slippery terrain. If the sealant you use stops working for any reason, you can still use a conventional tube to get home.
Tubeless haven't yet had the same impact on the road as they have off-road. The advantages of road tubeless are the same as off-road: no pinch flats, lower tire pressures, and very low rolling resistance. Tubeless tires are harder to install and inflate than regular clinchers, and the weight savings by not using a tube is potentially significant -- however, at this point, tubeless tires are not as light as the top standard clinchers.