Lee DeForest added the grid to the diode in 1908 and at that time radio signals below 200 meters (today we would say above 1.5 MHz remember as frequency goes up wave length goes down) was considered very high frequencies. When Amateur Radio Operators licenses became required in 1912 it was believed useful radio communications could only be done on 3,000 to 300 meters (100 to 1,000 KHz) so the ham radio operators were restricted to 200 meters and above because they would only be able to communicate about 25 miles (40 KM) or less.
Amateur radio operators proved the value of those frequencies above 1.5 MHz and continued to press the limits higher with very impressive results. The triode tube was proving it self but as the frequencies continued to go up and the power demands on the triode vacuum tube increased new problems
developed. The capacitive reactance of the interelectrode capacitance decreased as the frequency increased so as more power and higher frequencies were being attempted the triode proved to be unstable or might even go into self oscillation at undesired frequencies; and with an amplifier any frequency of self oscillation is an undesired frequency.
A capacitor is any two conductors separated by an insulator so any time there is a potential difference between the plate and the grid, the plate and the cathode, or the grid and the cathode there is capacitance. The results of this interelectrode capacitance are known as the Miller Effect, named for John Miller who described the effect in triodes that limited their high-frequency usefulness in 1920. If you would like to learn more about the Miller Effect http://en.wikipedia.org/wiki/Miller_effect has an excellent article but it goes beyond the scope of this post.
One solution was to use negative feedback (a small portion of output from the tube fed back into the input 180 degrees out of phase) equal to the positive
feedback caused by the interelectrode capacitance. This process is called neutralization. While this worked it reduced the overall gain (amount of amplification) of the circuit and it can be a tricky adjustment.
Another way to reduce the effects of interelectrode capacitance was to use a grounded grid amplifier. As the name suggests the grid is at ground potential of incoming signal. The input is to the cathode and the output is off the plate. This amplifier has a low impedance input and a high impedance output. While the circuit is a good one and still used in ham radio linear amplifiers today it sacrifice gain.
Many efforts were tried with varying successes and failures. It was not until 1926 that Dr. Albert W. Hull and N. H. Williams were credited with inventing the tetrode (four electrodes) vacuum tube. There does seem to be some argument that Walter H Schottky invented the tetrode in 1919. It is true that Schottky did add a second grid to the triode but he had very limited success with it.
The vacuum tube then had a cathode, control grid, screen grid, and a plate. The control grid was closest to the cathode and did the amplifying. The screen grid was between the control grid and the plate; it had a positive DC bias, a zero ground potential at the frequencies being amplified, and acted as a shield between the plate and the grid to reduce the effect of the interelectrode capacitance.
The screen grid greatly improved the frequency response and the gain. Neutralization was still needed to maintain stability in some instantiates. While the tetrode was a great improvement it brought with it new problems.