We define a L-series for harmonic Maass forms and discuss their functional equations. A converse theorem for these L-series is given. As an application, we interpret as proper values of our L-functions certain important quantities that arose in works by Bruinier-Funke-Imamoglu and Alfes-Schwagenscheidt, and which they had philosophically viewed as “central L-values”. This is joint work with M. Lee, W. Raji and L. Rolen.