Although we cannot directly observe black holes because light cannot escape from them, we can observe the way black holes affect their surroundings. Black holes pull in surrounding dust and gas which when heated emit radio waves, visible light, x-rays and even gamma rays that we can detect. Also, we can  directly observe the accretion disk and the jets formed from black holes with modern telescopes such as the Hubble. 

Radio
 
 
 

X-Ray/Gamma Ray Emmission

    As you know, a black hole pull in surrounding matter such as gas and star dust which forms an accretion disk around its event horizon. The potential energy of this matter then converts into heat energy. Because of the black holes deep gravitational well, the matter is heated to superhot temperatures, which emits high energy X-rays or even gamma rays. This radiation can observed with modern X-ray telescopes. 
 

Gravitational Waves
    
    It is believed by some theorists that massive