Costa has been the primary target for Jose Mourinho since his failure to sign Wayne Rooney last summer. He scored 35 goals in 43 appearances for Atletico last season, which is six more than Chelsea’s three strikers managed. What's more, one of those goals ended the London club's Champions League run.
In that time, Atletico have been playing a counter-attacking game, similar to Chelsea under Mourinho. Costa fits the system well. He has the strength to hold up the ball, the skill to dribble through defences, and he is statistically much better than any of Chelsea’s current strikers.
However, as important as Costa was to Atletico breaking the Real Madrid/Barcelona duopoly at the top of La Liga, he does bring significant concerns with him to Stamford Bridge.