In this paper, Witkin and Baraff introduce their fast implicit cloth solver and demonstrate how using implicit methods can overcome performance problems in explicit methods. 

The main problem with accurately solving a cloth simulation is that the underlying model can become stiff, as they note, since cloth resists stretching, but is comparatively permissive in allowing bending or shearing motions. And as we learned, explicit methods do a poor job with stiff differential equations because they require lots of small timesteps in order to get an accurate result.

So they present an implicit solver that operates on springs defined over a set of triangles (removing topological restrictions that the cloth be a sheet). And they demonstrate the performance advantages of this solver over the then standard explicit methods.

It should be noted that their primary contribution isn't in using implicit methods per se, but in solving them using a modified conjugate gradient solver. The force matrix for cloth is usually very sparse, and unbanded, so such a solver is appropriate and will rapidly converge on a low-error solution.

Further, they deal with constraints with a clever hack whereby instead of adding forces to constrain motion, they instead add a ton of mass. This can wreck havoc on a conjugate gradient solver since the resulting equations don't produce a symmetric matrix. So they modify it to procedurally apply constraints during each conjugate gradient step.