Simultaneous machine translation models start generating a target sequence before they have encoded the source sequence. Recent approaches for this task either apply a fixed policy on a state-of-the art Transformer model, or a learnable monotonic attention on a weaker recurrent neural network-based structure. In this paper, we propose a new attention mechanism, Monotonic Multihead Attention (MMA), which extends the monotonic attention mechanism to multihead attention. We also introduce two novel and interpretable approaches for latency control that are specifically designed for multiple attention heads. We apply MMA to the simultaneous machine translation task and demonstrate better latency-quality tradeoffs compared to MILk, the previous state-of-the-art approach. We analyze how the latency controls affect the attention span and we study the relationship between the speed of a head and the layer it belongs to. Finally, we motivate the introduction of our model by analyzing the effect of the number of decoder layers and heads on quality and latency.