Validated conceptual multiple-choice surveys administered before and after instruction can be useful tools to gauge the effectiveness of curricula and pedagogical strategies. Here we discuss four 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 (IL) physics concepts by administering them to both IL and advanced-level (AL) students. The cross-sectional performance of students on these IL physics concepts reveals which concepts remain challenging for students past their first year of physics and how incorrect answers evolve from IL to AL. The QMFPS was used to investigate co-construction and construction of knowledge in advanced quantum mechanics courses. Students took the QMFPS individually and then in groups 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 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 determined which concepts were difficult for students and which were easier after working together without instructor feedback. Lastly, we discuss the STPFaSL-Long survey's development and validation involving IL 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.