Calcite is a semi-soluble mineral that can be considered one of the main problematic gangue phases for several different types of valuable sulfides and oxides. Since froth flotation is the main beneficiation technique for upgrading these valuable minerals, calcite flotation separation has been widely investigated. Semi solubility property of calcite makes its flotation complicated. Through the flotation process, calcium particles release cations into the pulp solution, generate similar surface properties throughout ore minerals, consume reagents, and lockdown flotation beneficiation. Over the years, to tackle this complexity, calcite reverse flotation (calcite depression) has become the main technique for its rejection; therefore, there is a gap in its direct flotation investigations. In addition, the low selectivity of the existing depressants enhanced the importance of detailed calcite surface chemistry analyses and the development of more selective depressants. These studies can use various cations and explore their interactions with calcite surface depression. Ultrasonic and leaching pretreatments have been reported to enhance calcite depression as well, although several rooms are still empty in this area. As a review article, this study generally discussed the existing challenges in detail and provided suggestions for future investigation in calcite flotation.