Source: www.senate.gov/legislative/cloture/clotureCounts.htm

This chart shows the sharp rise in the number of filibusters in recent years.

The blue bars indicate a Democratic majority - thus filibusters by Republicans.
The red bars indicate a Republican majority - thus filibusters by Democrats.

The numbers actually represpent cloture mostions. The Senate does not keep track of filibusters. Rather, it keeps track of cloture motions. Though not an exact representation of filibusters, it is the closest way to measure the number.