CMOS integrated circuits are almost exclusively used in modern computers and stuff because they're small and profitable. They also sometimes consume little power when doing nothing.
Digital circuits using bipolar junction transistors are usually TTL, and sometimes ECL, maybe even IIL.
But BJTs can also be arranged just like MOS devices. I mean, why not. So without further ado, here is a CBJTS inverter:
(Complementary Bipolar Junction Transistors with Schottky).
The Schottky diodes can of course be omitted, but they make the circuit faster.
I shoud really build some of these when I find some time, as simulations tell me it's interesting. Apparently it can switch in 20 nanoseconds, works with a 1 volt supply and draws between 1 and 2 milliamperes depending on temperature. I guess the supply voltage needs to raised a little bit above 1V if multiple-input logic functions such as NAND are to be implemented in the same way they're done in CMOS.
Anyway, it should be fun. Just try to pronounce "cbjts". It sounds and looks cool.