Test power, data volume, and test time have been long-standing problems for sequential scan based testing of system-on-chip (SoC) design. The modern SoCs fabricated at lower technology nodes are complex in nature, the transistor count is as large as billions of gate for some of the microprocessors. The design complexity is further projected to increase in the coming years in accordance with Moore's law. The larger gate count and integration of multiple functionalities are the causes for higher test power dissipation, test time and data volume. The dynamic power dissipation during scan testing, i.e. during scan shift, launch and response capture, are major concerns for reliable as well as cost effective testing. Excessive average power dissipation leads to a thermal problem which causes burn-out of the chip during testing. Peak power on other hand causes test failure due to power induced additional delay. The test failure has direct impact on yield. The test power problem in modern 3D stacked based IC is even a more serious issue. Estimating the worst case functional power dissipation is yet another great challenge. The worst case functional power estimation is necessary because it gives an upper bound on the functional power dissipation which can further be used to determine the safe power zone for the test. Several solutions in the past have been proposed to address these issues. In this thesis we have three major contributions: 1) Sequential scan chain reordering, and 2) JScan-an alternative Joint-scan DFT architecture to address primarily the test power issues along with test time and data volume, and 3) an integer linear programming methodology to address the power estimation problem. In order to reduce test power during shift, we have proposed a graph theoretic formulation for scan chain reordering and for optimum scan shift operation. For each formulation a set of algorithms is proposed. The experimental results on ISCAS-89 benchmark circuit show a reduction of around 25% and 15% in peak power and scan shift time respectively. In order to have a holistic DFT architecture which could solve test power, test time, and data volume problems, a new DFT architecture called Joint-scan (JScan) have been developed. In JScan we have integrated the serial and random access scan architectures in a systematic way by which the JScan could harness the respective advantages from each of the architectures. The serial scan architecture from test power, test time, and data volume problems. However, the serial scan is simple in terms of its functionality and is cost effective in terms of DFT circuitry. Whereas, the random ac-cess scan architecture is opposite to this; it is power efficient and it takes lesser time and data volume compared to serial scan. However, the random access scan occupies larger DFT area and introduces routing congestion. Therefore, we have proposed a methodology to realize the JScan architecture as an efficient alternative for standard serial and random access scan. Further, the JScan architecture is optimized and it resulted into a 2-Mode 2M-Jscan Joint-scan architecture. The proposed architectures are experimentally verified on larger benchmark circuits and compared with existing state of the art DFT architectures. The results show a reduction of 50% to 80% in test power and 30% to 50% in test time and data volume. The proposed architectures are also evaluated for routing area minimization and we obtained a saving of around 7% to 15% of chip area. Estimating the worst case functional power being a challenging problem, we have proposed a binary integer linear programming (BILP) based methodology. Two different formulations have been proposed considering the different delay models namely zero-delay and unit-delay. The proposed methodology generates a pair or input vectors which could toggle the circuit to dissipate worst power. The BILP problems are solved using CPLEX solver for ISCAS-85 combinational benchmark circuits. For some of the circuits, the proposed methodology provided the worst possible power dissipation i.e. 80 to 100% toggling in nets.