This interesting survey is concerned with properties of the Nevanlinna class of holomorphic functions versus the class \(H^\infty(\mathbb D)\) of bounded holomorphic functions in the unit disk. Formally defined as \[N=\Big\{f\in H(\mathbb D): \sup_{ 0 < r < 1} \int_0^{2\pi} \log^+|f(re^{it})|dt<\infty\Big\},\] it coincides with quotients \(f/g\) of bounded holomorphic functions, where \(g\) is zero-free. Considered are interpolating sequences, sets of determination, ideal theoretic questions (Corona theorem and finitely generated ideals), invertibility in quotient algebras. Many of the classical results for \(H^\infty\) have their analogues in \(N\): the role of uniform bounds is now played by a specific growth control via positive harmonic functions. These were mainly developed by the authors in cooperation with A. Hartmann and A. Nicolau. There are also several differences which are recapped by the authors: for instance if \(b\) is a Blaschke product, then the corona theorem holds in the quotient space \(N/bN\) if and only if \(b\) is a finite product of Blaschke products whose zeros are interpolating for \(N\). This dramatically contrasts the situation for quotient algebras \(H^\infty/bH^\infty\), the theory of which was developed by P. Gorkin et al. [J. Funct. Anal. 255, No. 4, 854–876 (2008; Zbl 1161.46028)].