This is only half a question as you do not address what frequency, power level or beam characteristic and these all have an influence on the type of beam forming used.
However as an example, Ferrite phase shifters are used on older radar systems. Active steered electronic arrays which have individual amplifiers at each antenna element are used on newer systems.
Also, BFN's can be relatively simple or extremely complex. It depends on the details. One hint: you can't scan greater than the beamwidth (BW) of a single element without pattern distortion.
I need an overall view of BFN. I am not looking for a specific design or application. My main purpose is the information about the advantages and disadvantages of each kind and when we are going to use each one.
If you only want to form one beam, it's simple. Buy a power divider and hook up cables to the antenna array.
If you need more beams then the next choice is "Butler matrix" or "Blass Matrix" search these on the internet. They are cousins of each other. Most cell sites use a Butler Matrix.
Wider bandwith, use a 'microwave stripline lens' beamformer, often called a "Rotmen Lens", they can give you 2:1 or up to 5:1 bandwidth.
Narrower bandwith beamformers use a power divider with phase shifters.