Validated conceptual multiple-choice surveys administered before and after instruction in relevant concepts can be useful tools to gauge the effectiveness of curricula and pedagogical strategies. Here we discuss the use of four different validated surveys to investigate student understanding: The Energy and Momentum Conceptual Survey (EMCS), the Conceptual Survey of Electricity and Magnetism (CSEM), the Quantum Mechanics Formalisms and Postulates Survey (QMFPS), and the Survey of Thermodynamic Processes and First and Second Laws-Long (STPFaSL-Long). The EMCS and the CSEM were used to investigate progression in student understanding of introductory-level physics concepts by administering them to both introductory and advanced level students as a pre- and a post-test. The cross-sectional performance of students on these introductory level physics concepts reveals which concepts remain challenging for students past their first year of physics and how the most common incorrect answers may evolve on various questions from introductory to advanced levels. The QMFPS was used to investigate co-construction and construction of knowledge in advanced quantum mechanics courses. Students were asked to take the QMFPS individually and then in a group of 2-3 with no feedback on their initial performance. Co-construction occurred when all students in a group originally answered a question incorrectly on their own but answered it correctly as a group after discussion. Construction occurred when only one student answered a question correctly individually, but the group answered it correctly. By comparing construction and co-construction of knowledge, we were able to determine which concepts were difficult and which concepts were easier for students so that they could answer them correctly by working together without feedback from the instructor. Lastly, we discuss the development and validation of the STPFaSL-Long survey instrument. This survey instrument was administered as a pre- and post-test to introductory-level students, upper-division students in an upper-level thermodynamics course, and graduate students across many different universities. We discuss the context dependance of student responses along with student difficulties with thermodynamic variables and the first and second laws of thermodynamics. We used both written data and interviews from the STPFaSL survey instrument to investigate these issues. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]