In 1994, Lewis Wolpert wondered “Will the egg be computable? That is given a total description of the fertilized egg – the total DNA sequence and the location of all proteins and RNA – could one predict how the embryo will develop?”. In this review, we discuss what computing the embryo entails and explore how advanced imaging, single-cell genomics and physical measurements are changing our view of the embryo and enable the development of multi-scale computational models that are starting to explain in physical terms how the genome controls the dynamic behavior of each cell in a developing embryo.