This paper aims to present the literature related to the regulation of Type 1 Diabetes Mellitus (T1DM) via positive control and constrained control. This idea of positive control was derived because the control input (insulin) can only be infused/injected (one direction control). The main operation of insulin is to reduce glycemia back to euglycemia. If glycemia goes into hypoglycemia; the only possible way is to stop insulin injection temporarily, and the patient must take some carbohydrates to raise glycemia. Also, hyperglycemia can be treated by estimating the amount of meals taken by the patient using an estimator. Since meals are a positive factor, the controller gives an adequate positive action to eliminate the effect of meals. This paper reviews the research work related to regulating glycemia that considered the positivity of insulin as a control input. The impact of considering the positive control in the design is the fact that any negative decision will be cut off to zero. In such case, the system is left open-loop and will be out of control.