  In this review paper, we delve into the nascent field of molecular data
storage, focusing on system implementations and code constructions. We start by
providing an overview of basic concepts in synthetic and computational biology.
Afterwards, we proceed with a review of the diverse approaches followed to
implement such systems. In the process, we identify new problems in
communication and coding theory, and discuss some relevant results pertaining
to DNA sequence profiles, coded trace reconstruction, coding for DNA punchcard
systems and coding for unique reconstruction.
