A blockchain is a continually-extended chain of commitments
(well, a consensus-selected path in some continually-extended DAG)
Bitcoin commits to transactions, disallows conflicts, producing a system state (utxoset)

To verify the system state, obtain the consensus DAG and verify everything committed in it
(Alternately: have the DAG commit to the state and trust that "there wouldn't be consensus on an invalid state". Much much weaker security)
Not the only model: in Aug 2016 Tom Elvis Jedusor proposed "Mimblewimble", which drops tons of committed data
In Jan 2017 AP invented an atomic swap via "scriptless scripts"; lots of progress throughout 2017

Two stories to tell:
1. how Mimblewimble transactions are restricted and what this allows us to drop
2. how we can execute trustless contracts regardless (and therefore do it on less restricted blockchains w better privacy/efficiency and less coordination)