We report arrays of latching microfluidic valves based on shape memory polymers (SMPs), and show their applications as reagent mixers and as peristaltic pumps. The valve design takes advantage of the SMP's multiple stable shapes and over a hundred-fold stiffness change with temperature to enable a) permanent zero-power latching in either open or closed positions (>15 h), as well as b) extended cyclic operation (>3000 cycles). The moving element in the valves consists of a tri-layer with a 50 μm thick central SMP layer, 25 μm thick patterned carbon-silicone (CB/PDMS) heaters underneath, and a 38 μm thick styrene ethylene butylene styrene (SEBS) impermeable film on top. Each valve of the array is individually addressable by synchronizing its integrated local Joule heating with a single external pressure supply. This architecture significantly reduces the device footprint and eliminates the need for multiplexing in microfluidic large scale integration (mLSI) systems.