777 has three manual primary flight control law modes: Normal, Secondary, and Direct. Normal Mode is required to support autopilot engagement and/or flight director. C*U and envelope protection control laws are provided only in Normal Mode. Secondary Mode continues to use the same primary flight control computers (PFCs) as Normal Mode, but is much simplified due to detected loss of certain signals needed to support Normal Mode. Direct Mode has essentially the same functionality as Secondary Mode, but uses only the Actuator Control Electronics (ACE) computing hardware/software bypassing the PFCs. Normal Mode is maintained for loss of radio altitude, but reversion to Secondary Mode will occur if input signal selection / fault detection logic declares air data or inertial data invalid. (Note that redundancy supports continued operation in Normal Mode for loss of individual sources of either air or inertial data.)
There are two ways to get to 777 Direct Mode. The first is via pilot selection using overhead primary flight computer disconnect switch. The second is as a result of loss of valid commands from all three PFCs simultaneously. (Each PFC employs multiple redundant computing elements so that operation with a single PFC is permitted provided in-line monitoring continues to declare is commands to be valid.)
From the handling qualities / pilot training perspective 777 Secondary and Direct Modes are sufficiently similar to not require dedicated training with one vs. the other.
The story for 787 and the coming 777X with regard to primary flight control modes is similar to the current 777.