  Cryptocurrencies are distributed systems that allow exchanges of native (and
non-) tokens among participants. The complete historical bookkeeping and its
wide availability opens up an unprecedented possibility, i.e. that of
understanding the evolution of their network structure while gaining useful
insight on the relationships between user' behaviour and cryptocurrency pricing
in exchange markets. In this contribution we review some of the most recent
results concerning the structural properties of Bitcoin Transaction Networks, a
generic name referring to a set of different constructs: the Bitcoin Address
Network, the Bitcoin User Network and the Bitcoin Lightning Network. The
picture that emerges is that of system growing over time, which becomes
increasingly sparse and whose mesoscopic structural organization is
characterised by the presence of an increasingly significant core-periphery
structure. Such a peculiar topology is matched by a highly uneven distribution
of bitcoins, a result suggesting that Bitcoin is becoming an increasingly
centralized system at different levels.
