This book chapter is published open access.
In this article, aimed at a general mathematical audience, we have three goals. First, we give a brief account of the classical theory connecting primes, the Riemann zeta function, and the Möbius function. Second, we discuss the state-of-art results concerning primes, almost primes, and the Möbius function in short intervals. Third, we outline the most fundamental concepts underlying the proofs of such results.