Lab-on-chip (LOC) is recognised as one of the most affordable solutions for integrating electronics and fluidics devices. In this field, bonding plays a vital role because it provides the means for attaching multiple components onto a substrate, transforming them into a microfluidic circuit. Bonding is an integral step, especially when designing a device that is free from leakage and eventual clogging. A comprehensive review of the latest irreversible bonding technologies is discussed in this paper, in which the focus is on the layered microfluidic systems with large sensor arrays. This review covers microfluidic devices fabricated from a rigid-type glass–fibre-printed circuit board and a thermoplastic flexible printed circuit with 186 references whose development date back three decades ago. The bonding techniques are organised into the following four groups: (a) adhesive bonding, (b) thermal and solvent bonding, (c) surface modification and dry bonding and (d) photoresist groups. Other techniques are available beyond these groupings, but they can be classified into the nearest group to facilitate the discussion. This paper will benefit researchers and practitioners aiming to develop polymer-based LOC devices.