Mechanical metamaterials are manmade structures with counterintuitive mechanical properties that originate in the geometry of their unit cell instead of the properties of each component. The typical mechanical metamaterials are generally associated with the four elastic constants: Youngs modulus E, shear modulus G, bulk modulus K and Poissons ratio v. Here a clear classification of mechanical metamaterials is established based on the tuning elastic constants. Mechanical metamaterials can be divided into negative Poissons ratio auxetic metamaterials (υ<0, G>>K), pentamode metamaterials (G<<K), negative compressibility (-4G/3<K<0), pattern transformation with tunable stiffness (E), ultralight and ultrastiff lightweight (E/ρ), negative thermal expansion. Based on the lattice and chiral/antichiral structure, we review the architected mechanical metamaterials and unexplored properties. This provides a broad overview of significant potential mechanical metamaterials together with the upcoming challenges in the intriguing and promising research field.