This review aims to classify algorithms for intravenous insulin infusion according to design. Essential input data include the current blood glucose (BGcurrent), the previous blood glucose (BGprevious), the test time of BGcurrent (test timecurrent), the test time of BGprevious (test timeprevious), and the previous insulin infusion rate (IRprevious). Output data consist of the next insulin infusion rate (IRnext) and next test time. The classification differentiates between “ IR ” and “ MR ” algorithm types, both defined as a rule for assigning an insulin infusion rate (IR), having a glycemic target. Both types are capable of assigning the IR for the next iteration of the algorithm (IRnext) as an increasing function of BGcurrent, IRprevious, and rate-of-change of BG with respect to time, each treated as an independent variable. Algorithms of the IR type directly seek to define IRnext as an incremental adjustment to IRprevious. At test timecurrent, under an IR algorithm the differences in values of IRnext that might be assigned depending upon the value of BGcurrent are not necessarily continuously dependent upon, proportionate to, or commensurate with either the IRprevious or the rate-of-change of BG. Algorithms of the MR type create a family of IR functions of BG differing according to maintenance rate (MR), each being an iso-MR curve. The change of IRnext with respect to BGcurrent is a strictly increasing function of MR. At test timecurrent, algorithms of the MR type use IRprevious and the rate-of-change of BG to define the MR, multiplier, or column assignment, which will be used for patient assignment to the right iso-MR curve and as precedent for IRnext. Bolus insulin therapy is especially effective when used in proportion to carbohydrate load to cover anticipated incremental transitory enteral or parenteral carbohydrate exposure. Specific distinguishing algorithm design features and choice of parameters may be important to establish freedom from hypoglycemia, eliminate the need for administration of concentrated dextrose during euglycemia, control variability within the treatment course of individual patients, achieve adaptability to differing blood glucose targets, and minimize variability of glycemic control between treatment courses of different patients or patient populations. Areas for future work include the reduction of nursing burden, the development of a theory that will account for lag time of interstitial monitoring and pharmacodynamic delay of insulin action, and management strategies for the narrow euglycemic range. It is hoped that hypoglycemia and variability of control will become negligible problems, and that fear of hypoglycemia no longer will deflect investigators and caregivers from providing optimal glycemic management.