On a new layer create a rectangle and apply a gradient fill of your choice to it.
Create a new layer. On this layer create another rectangle and fill it with black & white gradient.
Go to Object - Envelope Distort - Make with Wrap and choose Arc as a style. I used bend 35%.
Rotate the figure in a way you like, change it's blend mode to Screen (Transparency palette) and Opacity to ~30%.
On a new layer create another rectangle and fill it with either black & white gradient or choose any other color instead of white. I choosed a light yellow.
Go to Object - Envelope Distort - Make with Wrap and choose, again, Arc as it's style with bend -35% this time. Change the object's Blend mode and Opacity as shown on the picture (Screen 40%). Rotate the object any way you like.
If you are not happy about the gradient you may always edit it. On the image below you can see how to do it. When you are done with the gradient color, do not forget to switch back to Edit the Object mode
Copy the object (Cntr+C or Command+C) and Paste it on a new layer. Change the gradient color to black & white.
Now we need to create an opacity mask for this object.
Draw a circle and apply a radial black & white gradient to it. Please note, that you need to use "Registration color" instead of simple black in the gradient.
Select both - the object we pasted on the layer first and the circle, and choose Make Opacity Mask from the Transparency panel menu.
Now the band will look like this:
You may always change the opacity mask's gradient or move it around by clicking on the mask icon in the Transparency panel, don't forget to unlink the mask from the object otherwise you will be moving both - object and it's mask - at the same time.
When you are happy with the result just click on the object icon in the Transparency panel to be able to work with the object itself.
Copy the band (along with it's mask) and past to a new layer. Rotate it in a way you like.
Repeat step 12.
Go to the Layer 3 (the first band we created). We will add some shining to it. Firstly, copy the band and paste it to the new layer, change the band's blending mode to normal and make sure that "registration" black color is used in the gradient.
Draw an ellips and fill it with black (registration) & white radial gradient, change it's Blending mode to Screen and Opacity to ~30% and place the ellips under the band.
Select both - the elips and the band and Make Opacity Mask
On a new layer create an elips and fill it with b&w gradient (remember using registration black).
Then apply the same Opacity mask as we did in Steps 14-16.
When you do any transformations to the elips (and in general to any object that has an Opacity mask) remember unlink the object from it's mask, otherwise you will end up transforming/moving both.
Here is what we've got after Step 18:
Now we may create the same shining edges on some other bands. For doing this select another band (Layer 7) and copy & past it to a new layer. Because we applied opacity mask to this band we need to release it first to be able to use it as a new opacity mask.
Repeat Steps 15-18 for this band and for the band on the Layer 6.
Now we need to tidy up our art board. Select all the objects on all the layers except for the background layer and group them (Cntrl+G / Command+G). Delete all empty layers.
Create a rectangle (above the grouped objects) with no fill and no stroke. Select all and Make a Clipping Mask (Cntrl+7 / Command+7). Congratulations! We are done.
Here it is - our nicely done abstract background ;)