This thesis deals with the design of two-axis displacement-amplifying compliant mechanisms (DaCMs) using topology optimization. The two-axis compliant mechanisms considered here are XY positioners and two-axis inertial sensors. A building block approach, with several single-axis DaCMs as building blocks, is used to conceive designs of compliant platforms that provide two orthogonal and independent movement of a common platform. Spring-mass-lever (SML) models of these designs are developed to simplify the analysis and design of the complicated arrangements of building blocks. The XY positioners designed in this work have perfectly de-coupled motion without compromising on the frequency; the best design of the stage has a displacement amplification of five resulting in the enhanced range of 4.2 % of the mechanism size–a significant improvement from the 1.67 %, the maximum range of the designs reported so far. Nearly 100% improvement is observed in the sensitivity of the two-axis accelerometer as compared with an existing design that occupied the same area. Multiple prototypes of XY positioners were fabricated on polypropylene sheets using CNC machining; and on spring steel and aluminium using wire-cut electro discharge machining. Mask layouts for two-layer two-axis accelerometers are designed for micro-fabrication using reactive ion etching and wafer bonding.