Monica left her family prior to the series starting, something that all the Gallagher children resent her for to some degree (Fiona and Lip especially). At the time the older kids were 19 (Fiona), 15 (Lip), & 13 (Ian).
Although Monica wasn't exactly a good person, it is showed that she always means well for her family. Due to her bipolar disorder and her addiction to drugs and alcohol, she is often unable to control herself, but at least tries to do what she thinks will benefit the Gallaghers.
After one final return in Season 7, it is revealed that she has Brain damage. Her death is shown in Happily Ever After when Frank is trying to wake her up, unsuccessfully. After dying, she passed on $70000 worth of drugs to her family, one final attempt at fixing the broken bond between her and them.
She is later buried, after her death (obviously), in her wedding dress and with two pounds of crack in her coffin.
Monica appears at the end of Season 1 after another of Frank's money making schemes and it is revealed that Monica is bisexual and dating a proud black lesbian called Roberta (but prefers to be called Bob). Roberta threatens the Gallagher clan with taking Liam to live with her and Monica as he needs to be raised by a black parent.
She comes back to live with the family in Season 2, saying she is back for good. During Season 2 episode Hurricane Monica, it is revealed that she suffers from bipolar disorder but does not take her medication. Her recent bad decisions and discontinuation of taking her medications lead to her attempting suicide but the family managed to get her to hospital in time to save her. When she was physically recovered she was moved to a psychiatric ward, where Debbie attempted to break her out. The three Gallaghers, along with another patient who claimed to have shot her husband 26 times, managed to escape the hospital together. But once out, Monica and the other patient drove away alone, with Monica shouting her love for Debbie as she went.
Monica is mentioned in Season 4 after it is discovered Ian has been staying with her after running away from the Gallagher home. They live in a old, damp, damaged house with an old woman. After Lip and Debbie arrive looking for Ian, they are told Monica no longer lives there with Ian anymore. During this season, Ian begins showing mental health issues very similar to his mother which would explain his desire to find her again.
After hearing Ian has been diagnosed with bipolar disorder, she takes Ian on an adventure around Chicago.
In season 7, she helps Debbie get Frances back and reveals to Frank that she has a brain aneurysm that she may have gotten from an infected needle. After a hangover, Frank tries to wake her up and realizes that she has died.