There are a number of testability considerations for VLSI design, but test coverage, test time, accuracy of test patterns and correctness of design information for DFD (Design for debug) are the most important ones in design with embedded memories. The goal of DFT (Design-for-Test) is to achieve zero defects. When it comes to the memory subsystem in SOCs (system on chips), many flavors of memory BIST (built-in self test) are able to get high test coverage in a memory, but often, no proper attention is given to the memory interface logic (shadow logic). Functional testing and BIST are the most prevalent tests for this logic, but functional testing is impractical for complicated SOC designs. As a result, industry has widely used at-speed scan testing to detect delay induced defects. Compared with functional testing, scan-based testing for delay faults reduces overall pattern generation complexity and cost by enhancing both controllability and observability of flip-flops. However, without proper modeling of memory, Xs are generated from memories. Also, when the design has chip compression logic, the number of ATPG patterns is increased significantly due to Xs from memories. In this dissertation, a register based testing method and X prevention logic are presented to tackle these problems. An important design stage for scan based testing with memory subsystems is the step to create a gate level model and verify with this model. The flow needs to provide a robust ATPG netlist model. Most industry standard CAD tools used to analyze fault coverage and generate test vectors require gate level models. However, custom embedded memories are typically designed using a transistor-level flow, there is a need for an abstraction step to generate the gate models, which must be equivalent to the actual design (transistor level). The contribution of the research is a framework to verify that the gate level representation of custom designs is equivalent to the transistor-level design. Compared to basic stuck-at fault testing, the number of patterns for at-speed testing is much larger than for basic stuck-at fault testing. So reducing test and data volume are important. In this desertion, a new scan reordering method is introduced to reduce test data with an optimal routing solution. With in depth understanding of embedded memories and flows developed during the study of custom memory DFT, a custom embedded memory Bit Mapping method using a symbolic simulator is presented in the last chapter to achieve high yield for memories. / text