There have been a number of variants of LSTM cells proposed during recent years. Two of them are really popular. Peephole LSTM allows the gate layers to look at the cell state, as depicted in the following figure with dotted lines, while Gated Recurrent Units (GRUs) merge the hidden state and the cell state into one single channel of information.

Again, both GRUs and Peephole LSTM can be used as a blackbox drop-in for standard RNN cells with no need to know the underlying math. Both cells can be used for solving the problem of vanishing gradients and can be used for building deep neural networks: