Recent studies find interannual (i.e., 3 to 7 year), decadal (i.e., 9 to 13 year), and interdecadal (i.e., 18 to 23 year) periodicities, and a trend dominating global sea surface temperature (SST) and sea level pressure (SLP) variability over the past hundred years, with the interdecadal signal dominating sub-El Niño-Southern Oscillation (ENSO) frequencies. We isolate interdecadal frequencies in SST and SLP records by band passing with a window admitting 15 to 30 year periods. From 1900 to 1989, the rms of interdecadal-filtered SST and SLP anomalies is largest in the extratropics and eastern boundaries. First-mode empirical orthogonal functions (EOFs) explain about half the interdecadal variance in both variables, with the tropical warm phase peaking near 1900, 1920, 1940, 1960, and 1980. From 1955 to 1994, EOF spatial patterns of interdecadal SST, SLP, and 400m temperature (T400) anomalies reveals global reflection symmetries about the equator and global translation symmetries between ocean basins, with tropical and eastern ocean SSTs warmer (cooler) than normal, covarying with stronger (weaker) extratropical westerly winds, cooler (warmer) SSTs in western-central subarctic and subantarctic frontal zones (SAFZs), stronger (weaker) subtropic and subarctic gyre circulations in North Pacific and North Atlantic Oceans, and warmer (cooler) basin and global average SSTs of 0.1°C or so. Evolution of interdecadal variability from the tropical warm phase to the tropical cool phase is propagative, also characterized by reflection and translation symmetries. During the tropical warm phase, cool SST anomalies along western-central SAFZs are advected slowly eastward to the eastern boundaries and subsequently advected poleward and equatorward by the mean gyre circulation, the latter conducting extratropical SST anomalies into the tropics. A delayed action oscillation model is constructed that yields the quasiperiodicity of interdecadal variability in a manner consistent with these global symmetries in both pattern and evolution.