From a programming perspective, Alan Turing's epochal 1936 paper on computable functions introduced several new concepts, including what is today known as self-interpreters and programs as data, and invented a great many now-common programming techniques. We begin by reviewing Turing's contribution from a programming perspective; and then systematize and mention some of the many ways that later developments in models of computation (MOCs) have interacted with computability theory and programming language research. Next, we describe the ‘blob’ MOC: a recent stored-program computational model without pointers. In the blob model, programs are truly first-class citizens, capable of being automatically compiled, or interpreted, or executed directly. Further, the blob model appears closer to being physically realizable than earlier computation models. In part, this is due to strong finiteness owing to early binding in the program; and a strong adjacency property: the active instruction is always adjacent to the piece of data on which it operates. The model is Turing complete in a strong sense: a universal interpretation algorithm exists that is able to run any program in a natural way and without arcane data encodings. Next, some of the best known among the numerous existing MOCs are described, and we develop a list of traits an ‘ideal’ MOC should possess from our perspective. We make no attempt to consider all models put forth since Turing's 1936 paper, and the selection of models covered concerns only models with discrete, atomic computation steps. The next step is to classify the selected models by qualitative rather than quantitative features. Finally, we describe how the blob model differs from an ‘ideal’ MOC, and identify some natural next steps to achieve such a model.