What is Log-Domain Filtering?
For very low supply voltages (1V or even lower) we can use the principle of analog signal processing in the "log domain". Using this principle, the exponential current-voltage characteristic of bipolar transistors (for very small currents) or of MOSFETs (sub-threshold region) is exploited.

The principle is based on a kind of "companding": The input signal is a current, which produces a "compressed" voltage in the log-domain - and after signal processing in this domain (amplification, intergation, filtering) the voltage signal is expanded and transferred back again into a current using the exponential characteristic of a transistor (inverse operation if compared with the input expansion).

In all cases, log-domain signal processing is realized in form of integrated circuits only. And as the main advantage very low supply voltages are allowed.     

Literature: 

Here is a good introductory text:

http://bioelectronics.tudelft.nl/~wout/documents/iscas20022.pdf