All experiments undertaken to find the "ether", the substance that is the carrier of light and other electromagnetik waves, have indicated that there most probably is none at all.

Why then don't the physicists abandon the wave concept and stick to the photon concept only? Apparently, some phenomens can be explained only by treating light as a wave.

Moreover, I remember having read that other particles, such as electrons, also behave like waves in some experiments.

Light is a strange thing; it can be seen as a wave or a particle, depending on which experiment you are doing, and what you are measuring.

If you are looking at the Photo-Electric effect for example, then light will appear to be made up of Quanta/Photons (units of energy), this is a quality of particles.

If, however you are looking at Light in a diffraction experiment then it will appear to interfere with itself, a property of waves.

All waves are traveling energy, moving through some medium, for example water. A water wave is made up of molecules of water that vibrate at right angles to the direction of the waves motion.  Light waves are different in that  they do not require a medium to travel through. This is most evident when they travel through a vacuum. A light wave is made of energy in the form of electric and magnetic fields that are vibrating at right angles to each other.