Alternating sign matrices are certain {0,1,-1}-matrices known to be equinumerous with plane partitions in the totally symmetric self-complementary symmetry class (TSSCPP), but no meaningful bijection is known. In joint work with Daoji Huang, we give such a bijection in the reduced, 1432-avoiding case, using the bijection of Gao and Huang between reduced bumpless pipe dreams and reduced pipe dreams. In joint work with Mathilde Bouvel and Rebecca Smith, we discuss the related notion of key-avoidance in alternating sign matrices. In joint work with Vincent Holmlund, we transform TSSCPPs to {0,1,-1}-matrices we call magog matrices, and investigate their enumerative and geometric properties.