In this talk, I’ll describe a braid word theoretic property, called “twist positivity”, which often puts strong restrictions on quantitative and geometric properties of a braid. I’ll describe some old and new results about twist positivity, as well as some new applications towards knot concordance. In particular, I’ll describe how using a suite of numerical knot invariants (including the braid index) in tandem allows one to prove that there is an infinite family of L-space knots (containing all positive torus knots and also an infinite family of hyperbolic knots) where every knot represents a distinct smooth concordance class. This confirms a prediction of the slice-ribbon conjecture. Everything I’ll discuss is joint work with Hugh Morton. I will assume little background about knot invariants for this talk – all are welcome!