TITLE: Status of PL topology
QUESTION [56 upvotes]: I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. I'd really want to know the state of the question, since I'm self-studying the material for pleasure and I don't have anyone to talk about it. Please feel free to close this post if you think the topic is not appropriate for this site.    
I'm starting to learn about geometric topology and manifold theory. I know that there are three big important categories of manifolds: topological, smooth and PL. But I'm seeing that while topological and smooth manifolds are widely studied and there are tons of books about them, PL topology seems to be much less popular nowadays. Moreover, I saw in some place the assertion that PL topology is nowadays not nearly as useful as it used to be to study topological and smooth manifolds, due to new techniques developed in those categories, but I haven't seen it carefully explained.
My first question is: is this feeling about PL topology correct? If it is so, why is this? (If it is because of new techniques, I would like to know what these techniques are.)
My second question is: if I'm primarily interested in topological and smooth manifolds, is it worth to learn PL topology?
Also I would like to know some important open problems in the area, in what problems are mathematicians working in this field nowadays (if it is still an active field of research), and some recommended references (textbooks) for a begginer. I've seen that the most cited books on the area are from the '60's or 70's. Is there any more modern textbook on the subject?
Thanks in advance.

REPLY [7 votes]: These questions are ok, but it is important to understand 
as much as you can about manifolds.
 For each of the categories:
 a] Homotopy Types satisfying Poincaré Duality...
 b] Topological Manifolds... 
 c] Sobolev Manifolds eg Quasiconformal or  Lipschitz Manifolds...
 d] Piecewise Linear or Piecewise Differentiable Manifolds...
 e] C1, C2,...C-infiniy = Smooth Manifolds...
 f] Real Analytic Manifolds...
 g] Real Algebraic Manifolds...
    The types with canonical coordinates:::
 h] Poisson Manifolds...
 i] Symplectic Manifolds...
 j] Complex Manifolds...
 k] Generalized Complex-Symplectic manifolds...
 l] Geometrized Three-Manifolds... 
  One knows contexts where each of these categories are particularly useful.
  [Dennis Sullivan]