This talk is a survey of open questions regarding the performance of algorithms in the literature to attack lattice-based cryptosystems. These algorithms are normally developed in layers as (1) SVP attacks, (2) approximate-SVP attacks, (3) cryptosystem attacks. The primary emphasis in this talk is on interesting problems that arise between the second and third layers, such as hybrid attacks (combining combinatorial techniques with lattice techniques) and optimizations within a large space of choices of lattices to use in an attack.