Microwave-assisted catalytic pyrolysis (MACP) is one of the emerging technologies for efficiently converting the solid biomass residues to valuable products, including liquid bio-oil and solid biochar. However, due to the poor dielectric properties, low thermal-conductivity, and complex compositions of biomass feedstock, two major technical challenges of biomass MACP technologies are how to heat biomass efficiently by microwave, and how to tune the pyrolysis process to improve the quality of products by catalysis. In the literature, direct, indirect as well as hybrid (localized and segregated) heating modes have been explored to improve the heating performance of microwave reactors, and in-situ, ex-situ and hybrid (dual, layered and series) catalyst configurations have been applied using different microwave absorbents and catalysts. In this review, those heating and catalysis strategies are systematically and critically reviewed (data from about 80 lab-scale studies and 1 pilot-scale unit) to reveal their differences in terms of heating efficiency and product qualities. For some biomass feedstock with high dielectric properties or under high electromagnetic field, direct heating without the use of microwave absorbent could be used. Indirect heating, on the other hand, can be used for all feedstock in which heat is transferred to the biomass via conduction/convection from high temperature surfaces heated by microwave. Hybrid heating with the use of microwave absorbents can greatly increase the local heating rate, promote the pyrolysis reaction rate and tune the distribution of pyrolytic products. In-situ catalysis shows the capability to tune the quantity and quality of both bio-oil and biochar by promoting direct interaction of catalyst and biomass via the pyrolysis vapour, while ex-situ catalysis exhibits a better potential to adjust the bio-oil yield and selectivity of desired compounds in bio-oil, and extends the catalyst life by avoiding the direct contact between biochar and catalyst. Hybrid catalytic mode combines in-situ and ex-situ catalysis in a more complex setup, but shows a great potential to regulate the yield, composition and properties of multiple products. Techno-economic-environmental assessments were also reported on the benefits of MACP processes with different heating and catalytic strategies, mostly based on the lab and limited pilot scale performance data. Future research and development should be focused on the evaluation of different absorbent-catalyst integration, heating-catalysis synergistic effect, optimization of products yields and properties, and how to scale up the MACP reactor technologies toward commercialization with continuous biomass feeding.