The Pioneer 10/11 spacecraft yielded the most precise navigation in deep
space to date. However, their radio-metric tracking data has consistently
indicated the presence of a small, anomalous, Doppler frequency drift. The
drift is a blue-shift, uniformly changing with a rate of ~6 × 10-9 Hz/s and can be interpreted as a constant sunward acceleration of
each particular spacecraft of aP = (8.74 ± 1.33) × 10-10 m/s2. The nature of this anomaly remains unexplained. Here we
summarize our current knowledge of the discovered effect and review some of
the mechanisms proposed for its explanation. Currently we are preparing for
the analysis of the entire set of the available Pioneer 10/11 Doppler data
which may shed a new light on the origin of the anomaly. We present a
preliminary assessment of such an intriguing possibility.