Graphitic nanowiggles (GNWs) are periodic repetitions of nonaligned finite-sized graphitic nanoribbon domains seamlessly stitched together without structural defects. These complex nanostructures have been recently fabricated [Cai et al., Nature (London) 466, 470 (2010)] and are here predicted to possess unusual properties, such as tunable band gaps and versatile magnetic behaviors. We used first-principles theory to highlight the microscopic origins of the emerging electronic and magnetic properties of the main subclasses of GNWs. Our study establishes a road map for guiding the design and synthesis of specific GNWs for nanoelectronic, optoelectronic, and spintronic applications.