What is the elegant way of applying function to two lists?

Question

I am interested in finding the most concise elegant way of doing the following: We have a function fun[x1,x2] and two lists:

ls1={a1,a2,a3,a4,......} 

and

ls2={b1,b2,b3,b4,......}

I want my result to be:

 Rslt={{{a1,fun[a1,b1]},{a1,fun[a1,b2]},{a1,fun[a1,b3]},.......},
        {{a2,fun[a2,b1]},{a2,fun[a2,b2]},{a2,fun[a2,b3]},.......}, 
        {{a3,fun[a3,b1]},{a3,fun[a3,b2]},{a3,fun[a3,b3]},.......},......}

Thanks for help.

Answer 1

Well, that's an easy one to write and maybe a bit harder to understand:

ls1 = {a1, a2, a3, a4};
ls2 = {b1, b2, b3, b4};

Outer[{#1, func[##]} &, ls1, ls2]