Diesel aircraft engines and are the light jets pushing out the twins?

A gas turbine scales up easily and but is nearly impossible to scale
down. The auto manuacturers found that out in the 1940s - remember
the "car of the future" on the covers of Popular Science et al?
Turbines for cars are further away now than they were 55 years ago.
The turbine suffers from excessive fuel consumption at part throttle
(the piston engine is incredibly flexible that way)and in smaller HP
installations.

So much of the useful load of an aircraft is fuel, that fuel
efficiency is very important for overall mission performance.

The problem of an engine is to find the most efficient way to expand a
certain flow rate of compressed hot gas to atmospheric pressures. A
turbine can do this with large mass flow rates, but as the flow rates
become smaller, the turbine speeds (rpm) must increase enormously and
the centrifugal accelerations get out of hand. On the other hand, a
piston can process an expansion efficiently with small flow rates.

Think of it this way - a model airplane engine can be made to run with
1/20 of a cubic inch (.049 cu inch to even .010 cu inch), but piston
engine aircraft became impractical above a few thousand HP. That is
the range of practicality for a piston concept.

An engineering prof once said - if the gas turbine had been invented
first, the piston engine would have been looked on an ingeneous
solution to the turbine's material and speed and power range problems.

Diesels may eventually make it. They have a weight problem that may
be offset by a lower specific fuel consumption, but for a given
operating condition, spark ignition engines can nearly approach the
consumption of diesels by using turbo compounding and operation only
at full throttle.