Advances in computational hardware has greatly expanded the power to collect and store data. With collection of greater data sets, comes greater difficulties in estimation, warranting more analysis and novel methods to handle. This is still true in threshold estimation, the estimation of discontinuities. To this end we present this body of work in thresholding problems in long data sequences and data with growing dimensions. The former setting, more commonly known as the change point problem, we introduce and analyze a method which can estimate change points with greater computational efficiency than existing procedures, without compromising the accuracy of the estimators. For the latter problem, also known as the change plane problem, we will study the case when the dimension of the problem grows with the sample size, a setting not well-studied in existing literature, and lay the groundwork with asymptotic results.