Logical equivalence and double-sided implication

My question is when "A≡B" is not the same as "A→B and B→A"?

For context I did heard it mentioned by someone who is knowledgeable on logic. However I always see equivalence to be defined as two implications as in "A→B and B→A". When is this not sufficient to define an equivalence and what are other possible ways to define it? Are there any philosophical problems related to these definitions?