  The theory of how low mass stars form from the collapse of a dense molecular
cloud core has been well-established for decades. Thanks to significant
progress in computing and numerical modelling, more physical models have been
developed and a wider parameter space explored to understand the early stages
of star formation more fully. In this review, I describe the expected physical
properties of the first and second core stages and how the inclusion of
different physics affects those predicted characteristics. I provide an
overview of chemical models and synthetic observations, looking towards the
positive identification of the first core in nature, which remains elusive.
However, there are a few likely candidate first cores, which are listed, and I
briefly discuss the recent progress in characterising the youngest protostellar
sources. Chemistry will be instrumental in the firm identification of the first
core so we require robust theoretical predictions of the chemical evolution of
protostellar cores, especially of the first and second core outflows. Looking
ahead, simulations can shed light on how the protostellar collapse phase shapes
the evolution of the protostellar disc. Simulations of dust evolution during
protostellar core collapse show there is significant enhancement in grain size
and abundance towards the centre of the core. Chemical models show that the
warm, dense conditions of the first core drive chemical evolution. There is a
wide scope for further study of the role that the first and second core stages
play in determining the structure and composition of the protostellar disc and
envelope and, of course, the eventual influence on the formation of planets.
