Bodyweight exercises can be very useful in conditioning or building muscular endurance. By gradually progressing to skills the are more muscularly challenging, or using added weight (ex. a weighted vest) progressive overload can be achieved and you can get stronger. Some examples and tutorials can be seen here:
Tutorials
However there are a number of limitations. First, there is no bodyweight equivalent to exercises like deadlifts or squats...pistols just don't cut it when it comes to training the posterior chain...and eventually you'd have to add weight to pisols anyway. Second, barbells allow for a greater precision of loading...I can adjust how much I"m lifting to within 0.5kg (although usually percision to that degree isn't important), this makes it easy to train an exercise at varying intensities and rep ranges, and it also means I can always add more weight...you never get to strong to make strength gains with a barbell.
So you definitely can make use of bodyweight skills...if your progressing to being able to do an iron cross (or whatever) you are getting stronger. But don't limit yourself to soley bodyweight exercises. And definitely get your squats in.