We study the anatomy of four widely used institutional trading algorithms representing $675 billion in demand from 961 institutions. Parent orders generate hundreds of child orders which strategically employ price, time-in-force, and display priority rules to navigate the tradeoff between trading and minimizing transaction costs. Child orders incur price impact at the time they are submitted regardless of whether or not they are filled, and even when passively priced. Child orders are grouped in strategic runs that oscillate between the aggressive or passive side of the spread. Child-level price, time-in-force, and display choices aggregate up to parent-level trading costs.