Despite being perceived to be a relatively innocuous pathogen during its circulation in Africa in the 20th century, consequent outbreaks in French Polynesia and Latin America revealed the Zika virus (ZIKV) to be capable of causing severe neurological defects. Foetuses infected with the virus during pregnancy developed a range of pathologies including microcephaly, cerebral calcifications and macular scarring. These are now collectively known as Congenital Zika syndrome (CZS). It has been established that the neuropathogenesis of ZIKV results from infection of neural progenitor cells in the developing cerebral cortex. Following this, two main hypotheses have emerged: the virus causes either apoptosis or premature differentiation of neural progenitor cells, reducing the final number of mature neurons in the cerebral cortex. This review describes the cellular processes which could potentially cause virus induced apoptosis or premature differentiation, leading to speculation that a combination of the two may be responsible for the pathologies associated with ZIKV. The review also discusses which specific lineages of the ZIKV can employ these mechanisms. It has been unclear in the past whether the virus evolved its neurotropic capability following circulation in Africa, or if the virus has always caused microcephaly but public health surveillance in Africa had failed to detect it. Understanding the true neuropathogenesis of ZIKV is key to being prepared for further outbreaks in the future, and it will also provide insight into how neurotropic viruses can cause profound and life-long neurological defects.