 There are three main motives for reformulating conventional QFT. The first motive is operationalism, the second one mathematical rigour and the third one finding a way to deal with the availability of inequivalent Hilbert space representations for systems with an infinite number of degrees of freedom, such as fields. While in principle the three motives are independent of one another there are multiple interconnections in their actual implementation. One way in which the three motives are connected is the following: In QFT the quests for operationalism and mathematical rigour seem to go hand in hand, i.e. the best means to achieve one is also the best way to achieve the other. Moreover, it leads to an algebraic formulation that avoids privileging one amoung various available inequivalent representations, which tacitly happens in conventional QFT.