The past decade has seen significant progress on the understanding of universality of various eigenvalue statistics of random matrix theory. However, the behavior of certain ``extremal'' or ``critical'' observables is not fully understood. Towards the former, we discuss progress on the universality of the largest gap between consecutive eigenvalues. With regards to the latter, we discuss the central limit theorem for the eigenvalue counting function, which can be viewed as a linear spectral statistic with critical regularity and has logarithmically growing variance.