Changes in the gut microbiome can affect cognitive and psychological functions via the microbiota–gut–brain (MGB) axis. Probiotic supplements are thought to have largely positive effects on mental health when taken in sufficient amounts; however, despite extensive research having been conducted, there is a lack of consistent findings on the effects of probiotics on anxiety and depression and the associated microbiome alterations. The aim of our study is to systematically review the most recent literature of the last 10 years in order to clarify whether probiotics could actually improve depression and anxiety symptoms. Our results indicate that the majority of the most recent literature suggests a beneficial role of probiotics in the treatment of depression and anxiety, despite the existence of a substantial number of less positive findings. Given probiotics’ potential to offer novel, personalized treatment options for mood disorders, further, better targeted research in psychiatric populations is needed to address concerns about the exact mechanisms of probiotics, dosing, timing of treatment, and possible differences in outcomes depending on the severity of anxiety and depression.