The most obvious invertibility problem that one has in mind is whether a given operator is invertible in an algebra of operators or whether a given function is invertible in an algebra of functions. A classical example (solved by Wiener ) is the question of whether the inverse of a non-vanishing function in the algebra of functions with absolutely convergent Fourier series belongs to the same algbera again. Indeed, there are many problems in analysis, operator theory and numerical analysis which turn out to be equivalent to invertibility problems in suitably associated Banach algebras. We shall give various examples to illustrate various invertibilty problems. The talk will be accessible to all (having basic knowledge on real analysis).