Tonight/tomorrow morning will mark the peak of the Quadrantid Meteor shower for 2015, thus marking the climax for the week-long event. Every December into January, Earth passes through the stretch of space junk shed by minor planet 2003EH, reaching the deepest concentration of debris tonight. According to some estimates, under ideal conditions (dark country skies), one can expect to see 100 meteors per hour. The reason the meteors are called Quadrantids is because the meteors seem to radiate from the now-defunct constellation Quadrans Muralis, which overlapped with Ursa Major and Bootes. The specific radiant location is right behind the Big Dipper's handle. The best time to view the shower is in the predawn hours as the radiant is at its highest then.
Don't want to stay up that late? Don't worry as the radiant is circumpolar/near enough so for us in the United States to have a chance to see the meteors all night, albeit that they will probably be low in a light dome. To improve odds of seeing meteors, travel out of the city and to the country if you can. In the suburbs, just going from the front to back yard can make a dramatic difference as this will eliminate glare from those pesky street/house lights to a large extent.
Unfortunately, this year's Quadramntid peak coincides with the Full Moon. The good news: even the Moon won't be able to drown-out the brightest meteors with all its light.
Note: unlike many meteor showers that have long peaks lasting all night, the Quadrantids have a sharp peak, which can often result in only a few meteors all night, a sudden outburst, and then very few thereafter.