When it comes to talking about denim, it is pretty essential to know that denim is a twill. Twill is a kind of weave with a pattern of diagonal parallel lines or rib. Now that you have that established, then you must also know that there are generally three different kinds of twill weaves used and they are all represented by the big three. Levis used right hand twill, Lee used left hand twill and finally Wrangler used broken twill - I'm sure that either of them have issued jeans using a different twill than the one stated, but that is the general norm.
Right-hand twill is the most commonly used weave for denim. This weave creates a twill, which lines go from left to right in a upward fashion. It has a slightly more pronounced twill feeling compared to the other two.
In left-hand twill the lines run from left to right in a downward fashion. There is a distinctly different feel to this type of twill than right-hand twill. It will often also have a softer hand and it will fade differently. The fades will be softer and slightly more vertical.
Back in the days the leg twist that we covered some time ago was considered a fault, which is why the broken twill weave was created. The weave changes direction, which creates a very recognisible zig-zag pattern on the back. It has been speculated that it is hard creating good, clear fades on broken twill, but old Wrangler jeans can be found with magnificent fades, so it is probably not the case, however it can be hard creating the same radient, clear fades that you can achieve with right-hand twill.