Lightweight mechanical metamaterials with exception specific stiffness and strength are useful in many applications, such as transportation, aerospace, architectures and etc. These materials show great potential in mechanical tasks where weight of the material is restrained due to economy or energy reasons. To achieve both the lightweight and the high specific mechanical properties, the metamaterials are often in form of periodic cellular structures with well-designed unit cells. The strategies in designing and improving such cellular structures become the key in the studies of such mechanical metamaterials. In this work, we use both experimental and numerical approaches while probing three types of mechanical metamaterials: i) composite bending dominated hollow lattices (HLs); ii) triply periodic minimal surfaces (TPMSs) and extended TPMSs (eTPMSs); iii) corrugated TPMSs. We have demonstrated a few strategies in designing and improving the specific stiffness or strength via these examples of mechanical metamaterials. Using carbon/ceramic composite in the bending dominated HLs, we prove that using the composite layered material against the single layer ceramic is effective in improving the specific mechanical performances of the mechanical metamaterials. Next, while studying the nature of TPMS, we discover that under isotropic deformation TPMSs are stretch dominated with no stress concentrations within the shell structure. They also have an optimal specific bulk modulus approaching the H-S upper bound. Furthermore, we establish a strategy to smoothly connect the zero-mean-curvature surfaces in TPMSs with the extension of zero-Gaussion-curvature surfaces, forming new ‘eTPMSs”. These new shellular structures trade off its isotropy and have improved specific Young’s modulus along their stiffest orientation compared to their TPMS base structures. Lastly, we introduce corrugated sub-structures to existing TPMSs to improve their mechanical properties, such as Young’s modulus, yield strength and failure strength in compression. It is found that the corrugated sub-structure can effectively suppress the local bending behavior and redirect crack propagation while such structures were under uniaxial compression.