Most data analytics systems that require low-latency execution and efficient utilization of computing resources, increasingly adopt two computational paradigms, namely, incremental and approximate computing. Incremental computation updates the output incrementally instead of re-computing everything from scratch for successive runs of a job with input changes. Approximate computation returns an approximate output for a job instead of the exact output. Both paradigms rely on computing over a subset of data items instead of computing over the entire dataset, but they differ in their means for skipping parts of the computation. Incremental computing relies on the memoization of intermediate results of sub-computations, and reusing these memoized results across jobs for sub-computations that are unaffected by the changed input. Approximate computing relies on representative sampling of the entire dataset to compute over a subset of data items. In this thesis, we make the observation that these two computing paradigms are complementary, and can be married together! The high level idea is to: design a sampling algorithm that biases the sample selection to the memoized data items from previous runs. To concretize this idea, we designed an online stratified sampling algorithm that uses self-adjusting computation to produce an incrementally updated approximate output with bounded error. We implemented our algorithm in a data analytics system called IncAppox based on Apache Spark Streaming. Our evaluation of the system shows that IncApprox achieves the benefits of both incremental and approximate computing.