Cosmological perturbation theory has been around for over 70 years and is the underlying theory for the interpretation of observations that have resulted in several Nobel prizes. Is there really anything new one can say about this field from a mathematical physics perspective? In this talk, which consists of two parts, I will try to convince you that the answer is yes. The first part deals with second order perturbations, which is a field that gives rise to notoriously messy equations. However, I will show that by using underlying physically motivated mathematical structures significant simplifications can be achieved, which give rise to new conserved quantities and simple explicit solutions in the so-called long wavelength limit, and for the currently dominating cosmological paradigm, the $\Lambda$CDM models. The second part is about a new research program where first order cosmological perturbation equations are reformulated as dynamical systems, which allows one to use dynamical systems methods and approximations, complementing previous investigations. Throughout the talk I will focus on ideas rather than technical details.