The lunar mare are basins that filled up with magma over the course of the Moon's history. So there were eruptions on the surface of the Moon at some point in time. When did the last eruption happen on the Moon?
The major mare forming eruptions occurred more than 3.5 billion years ago, but a paper Ages and stratigraphy of mare basalts finds that some volcanic basalts are as young as 1.2 billion years. However, it seems that impacts have been the only active geological process for a billion years, giving rise to the observation that just as complex life on Earth got started, the moon (geologically) died.
Braden et al. 2014 indicates that volcanism might have occurred on the Moon up to 100 million years ago. Most traces of volcanism such as the lunar mare are more than 3 billion years old. However, there are small patches that could have been caused by volcanism and that are ~100 million years old.