Aceves came to the Major Leagues in 2008 and pitched very well in four starts for the Yankees. He was converted to a full time relief pitcher and pitched well in 2009 and 2010 before a collarbone injury ended his season. In 2011, he signed with the Red Sox and appeared in 55 games, six of which were starts, to the tune of a 2.61 ERA. His 2012 season was significantly worse, as his ERA shot up to 5.36 while appearing in 69 games, serving as the Red Sox closer in Andrew Bailey's stead. During that time, Aceves reportedly had a tenuous relationship with Bobby Valentine and other members of the Red Sox organization, which carried into 2013.
In 2013, Aceves was ferried back and forth between Triple-A Pawtucket and the Red Sox, having compiled a 4.86 ERA in 11 appearances, including six starts. Aceves was then outrighted to Pawtucket on July 14 after clearing waivers and wasn't picked up by another team in the waiver process.
It is unclear to see if the Mets feel that Aceves could be a late-inning relief pitcher or if they just plan on bringing him in as a potential "mop-up man" candidate because of his versatility. In either event, Aceves has been described as a high-upside player, who may not have been able to put it all together, thus far.
Since Sandy Alderson began his tenure in New York, the Mets' bullpen has been pretty bad. While the team found its closer in Bobby Parnell and acquired Vic Black in the Marlon Byrd trade, there's a lot of uncertainty heading into next season. Although the Mets seem interested in bringing LaTroy Hawkins back after a very good season, the sides have not yet come to terms on a deal for 2014.