Long-period fibre gratings (LPFGs), which enable light coupling between the core mode and the cladding modes in a single-mode fibre at specific wavelengths (resonance wavelengths), form many useful devices for applications in optical communications and sensors. Although much research work has been carried out to improve the performance of LPFG-based devices, the structure and material constraints of an ordinary fibre have restricted the design and the functions of LPFG devices. Because thin-film optical waveguides can be fabricated into many different structures with a wide range of materials, long-period waveguide gratings (LPWGs), namely, long-period gratings fabricated in thin-film waveguides, have been proposed to extend the functionality of long-period gratings. This thesis focuses on the study of LPWG filters fabricated in polymer waveguides. The first part of the thesis is concerned with the study of the temperature sensitivity of an LPWG band-rejection filter fabricated in a polymer-clad ion-exchanged glass waveguide. Both experimental and simulation results show that the temperature sensitivity of an LPWG can vary over a wide range from a negative value to a positive value by controlling only the thickness of the waveguide cladding. The same waveguide structure and material system can therefore be used to implement a widely tunable filter or a temperature-insensitive filter. For example, the temperature sensitivity of a fabricated LPWG can be changed from +3.5 nm/°C to –0.3 nm/°C by changing its cladding thickness, which cannot be achieved easily with an LPFG. The second part of the thesis is devoted to the study of an LPWG bandpass filter. Like LPFGs, LPWGs are inherently band-rejection filters. To expand the usefulness of LPWGs, an LPWG bandpass filter is designed and demonstrated. The filter consists of two identical long-period gratings formed along a polymer channel waveguide with a gap introduced between the two gratings. A passband with a bandwidth of ~6 nm and a peak transmission of ~60% is achieved. The experimental results agree well with the simulation. The bandpass filter is thermally tunable over the C+L band with a temperature control of ~30 °C. Finally, an attempt is made to demonstrate an add-drop multiplexer using two vertically crossing dissimilar polymer channel waveguides, one of which contains an LPWG. Simulation shows that the crosstalk between the two output ports depends critically on the crossing angle of the waveguides. Preliminary experimental results are presented and discussed.