A fetal ultrasound (US) is a technique to examine a baby’s maturity and development. US examinations have varying purposes throughout pregnancy. Consequently, in the second and third trimester, US tests are performed for the assessment of Amniotic Fluid Volume (AFV), a key indicator of fetal health. Disorders resulting from abnormal AFV levels, commonly referred to as oligohydramnios or polyhydramnios, may pose a serious threat to a mother’s or child’s health. This paper attempts to accumulate and compare the most recent advancements in Artificial Intelligence (AI)-based techniques for the diagnosis and classification of AFV levels. Additionally, we provide a thorough and highly inclusive breakdown of other relevant factors that may cause abnormal AFV levels, including, but not limited to, abnormalities in the placenta, kidneys, or central nervous system, as well as other contributors, such as preterm birth or twin-to-twin transfusion syndrome. Furthermore, we bring forth a concise overview of all the Machine Learning (ML) and Deep Learning (DL) techniques, along with the datasets supplied by various researchers. This study also provides a brief rundown of the challenges and opportunities encountered in this field, along with prospective research directions and promising angles to further explore.