This Chapter Deals with Inelastic Processes that Occur in Collisions between Fast, Often Highly Charged, Ions and Atoms. Fast Collisions Are Here Defined to Be Those for Which V ∕ Ve ≥ 1, Where V is the Projectile Velocity and Ve the Orbital Velocity of This Electron. for Processes Involving Outer-Shell Target Electrons, This Implies V ≳ 1 a.u., or the Projectile Energy ≳25keV/a.m.u. for Inner-Shell Electrons, Typically, V ≳ Z2 ∕ N a.u., Where Z2 is the Target Nuclear Charge and N the Principal Quantum Number of the Active Electron. A Useful Relationship is V=6.35E/M, Where V is in A.u., E is in Me V, and M is in A.m.u. Fast Collisions Involving Outer-Shell Processes Can Be Studied using Relatively Small Accelerators, While Those Involving Inner-Shell Processes Require Larger Van De Graaffs, LINACs (Linear Accelerators), Etc. Because the Motion of the Inner-Shell Electrons is Dominated by the Nuclear Coulomb Field of the Target, and Because Transitions Involving These Electrons Take Place Rather Independently of What Transpires with the Outer-Shell Electrons, It Has Proven to Be Somewhat Easier to Understand One-Electron Processes Involving Inner-Shell Electrons. Thus, for A Long Time, A Great Deal of the Work on Fast Ion–atom Collisions Concentrated on Inner-Shell Processes Involving Heavy-Target Atoms. However, More Recently, New Experimental Techniques Have Led to A Shift of This Focus to Inelastic Processes Involving Light-Target Atoms. Furthermore, Present Investigations Go Beyond the One-Electron Picture to Include the Influence of the Electron–electron Interaction. the Present Chapter Outlines Some of the Developments in This Area over A Very Active Past Few Decades. the Literature is Vast, and Only A Small Sampling of References is Given. Emphasis is on Experimental Results (For the Theory, See Part D of This Book).