In 1937, Ettore Majorana introduced the concept of what are now fittingly called Majorana fermions -- fermionic particles that are their own antiparticles. Nowadays an active search for condensed-matter analogues of these elusive objects is well underway, motivated by both the prospect of revealing new facets of quantum mechanics and longer-term quantum computing applications. This talk will survey recent advances in this pursuit. In particular, I will describe strategies for "engineering" Majorana platforms from simple building blocks, preliminary experimental successes, and future milestones that reveal foundational aspects of Majorana physics directly relevant for quantum computation.