Contact structures on lens spaces are described by certain configurations of stacking objects called basic slices. Understanding them is helpful in 4-dimensional symplectic constructions. In joint work with Etnyre, understanding these configurations for virtually overtwisted lens spaces allowed us to classify their symplectic fillings, using a holomorphic filling method of Christian-Menke. In separate joint work with Etnyre-Min-Piccirillo, understanding the basic slice configurations for certain overtwisted lens spaces allowed us to construct symplectic caps for tight lens spaces, and build symplectic handlebody decompositions of $\mathbb{CP}^2$ corresponding to its almost toric fibrations.