Social media platforms have transformed traditional communication methods by allowing users worldwide to communicate instantly, openly, and frequently. People use social media to express their opinions and share their personal stories and struggles. Negative feelings that express hardship, thoughts of death, and self-harm are widespread in social media, especially among young generations. Therefore, using social media to detect and identify suicidal ideation will help provide proper intervention that will eventually dissuade others from self-harming, prevent suicide, as well as mitigate the spread of suicidal ideations on social media. Many studies have been carried out to identify suicidal ideation and behaviors in social media. This paper presents a comprehensive summary of current research efforts to detect suicidal ideation using machine learning algorithms on social media. This review encompasses thirty-seven studies investigating the feasibility of social media usage for suicidal ideation detection is intended to facilitate further research in the field and will be a beneficial resource for researchers engaged in suicidal text classification.