Interferometric Gravitational Wave Detectors, coming online lin late 2000, look for small space strains, leading to apparent motions of test masses of 10-19 m or less; isolation from other forces is crucial. They require a formidable vibration isolation level in a frequency range between few Hz and few kHz. The off-band residual motion must be kept below 10-12 m not to saturate the phase sensors. These exceptional requirements are met, in all degrees of freedom, with a chain of active and passive filters. The key isolation mechanism is the use of mechanical oscillators above their resonant frequencies, pendula horizontally, springs vertically. Very high quality pendular suspensions are needed at the mirror level to limit the thermal noise from fluctuations in the dissipation mechanisms. Off-band electromagnetic actuators on or near the mirror keep its magnitude of attenuation in the longitudinal direction. To provide the bulk of the attenuation, virtually all in the vertical direction, they are suspended from Seismic Noise Attenuation Systems. Attenuation filters, either active or passive, are chained, each providing 2 or 3 orders of magnitude of attenuation. Passive attenuation is obtained with springs and pendula. The vertical is the toughest direction to deal with because the oscillators also fight against gravity. The vertical attenuation requirements, although orthogonal to the beam direction, are only slightly less stringent than the vertical ones due to cross-couplings (Earth curvature is the source of one of them). High internal damping springs organized in hierarchical stacks are used in most early designs. More advanced designs increasingly rely on chains of filters equipped with high quality cantilever springs driven to low resonant frequencies by different mechanisms. The Quality Factors of each resonance are actively and/or passively spoiled at the chain suspension point. IN the latest designs, Ultra Low Frequency Oscillators filter out the microseismic and other low frequency perturbations. This paper addresses one approach to achieving the required seismic isolation level.