Gale Virtual Reference contains two good series that provide good thematic overviews of major plays. They are called Twenty-First Century Drama and Drama for Students. The easiest way to check your play is to do a search for your play title in their advanced search, and looks for entries in these two volumes.
Award lists can be one way to locate well-known 20th and 21st century plays.
For orienting a play in history, sometimes you don't need a really deep source, and reference sources are a great option here (particularly when you are starting out!). Here are some good ones that will introduce you to the time period of your play. From here you can dig deeper into the particular events or issues that seem most relevant to the play.
Try searching the name of your play and author together as well as the playwright alone to see generally what kind of literature exists.