A 3-dimensional del Pezzo fibration \( X\to C \) is one of the possible outcomes of the MMP. One aims to study the birational geometry of \( X \) in terms of the generic fibre \( X_{k(C)} \) and the base curve C. In positive characteristic, an additional difficulty arises: there are examples where all the fibres of a del Pezzo fibration are singular. In this talk, we explain these examples and describe how to bound such pathological cases. We extend two classical results of Enriques and Manin: (1) a 3-dimensional del Pezzo fibration over a curve, defined over an algebraically closed field, always admits a section; and (2) the total space is rational if the base curve is \( \mathbb{P}^1 \) and the anticanonical degree of a fibre is at least 5. This is joint work with H. Tanaka.