Most computer scientists and discrete mathematicians are familiar with computational complexity due to the famous P = NP conjecture. Some researchers have a more thorough understanding of the classes P, NP, and PSPACE since problems in logic, graph theory, and combinatorial optimization are often classified by their relationship to one of these classes. More recently, these concepts have found a wider audience through their application to puzzles and games. For example, it is known that the number puzzle Sudoku is NP-complete, whereas the box pushing game Sokoban is PSPACE-complete. In this talk we establish the computational complexity of several puzzles and games. We prove that two new paper and pencil puzzles are NP-complete. These puzzles are called Pencils and Sto-Stone, and were created by the Japanese publisher Nikoli that popularized Sudoku. We then prove that several puzzles that have been implemented as video games are PSPACE-complete. These games include a row shifting puzzle called MazezaM, a turnstile puzzle for the Nintendo Game Boy called Kwirk, and a puzzle called Switches that was invented by undergraduate student Jonathan Gabor while he was attending high school. Our reductions use conventional approaches such as Boolean Satisfiability, as well as some less conventional tools including Gray Codes, and the new Constraint Logic model pioneered by Hearn and Demaine in their influential textbook "Games, Puzzles, and Computation". The talk aims to be accessible to a wide audience, and hopes to encourage researchers to seek similar results for problems (or puzzles!) that are close to them. Most of the new results consist of joint work with undergraduate students at Bard College at Simon's Rock.