ReactJS: State is set back to initial value at each update

I just began ReactJS and I still have issue understanding states and props.

I'm trying to build a chat app using node.js, React and Socket.io. Everything is working fine on the server side, however, I have some hard time displaying the data.

Here's my issue: I have an app with three components, organized as below:

• Chat |- MessageList |- MessageInput

I want the Chat component to hold a list of messages, which is provided by the server and the messageInput component.

Since the Chat Component will hold the state, I have a constructor that initialize two variables. However, when I update these variables from the messageInput, the component is re-rendered, causing the constructor to be called again and the state re-initiliazed.

class Chat extends React.Component{
    constructor(){
        super()
        this.state = {
            messageList: [],
            username:null
        }
    }

I have noticed that the data retrieved from the server does not cause the state to be set to default. Input resets the value of the states in the Chat component, but seems to be working has intended: messages are send to the server, and displayed to the other clients.

I think I haven't quite understood how to properly set the state in a component. You'll find some of the client code below.

Thanks in advance!

const io = require('socket.io-client')
const socket = io.connect('localhost:4242')

class Chat extends React.Component{
    constructor(props){
        super(props)
        this.state = {
            messageList: [],
            username:null
        }
    }

    componentDidMount(){
        if (this.state.username == null){
            var user = prompt("Enter username:")
            this.setState(
                {username: user}, function(){
                    socket.emit('new_client', this.state.username)
                    this.addMessage({
                        text: this.state.username + " has entered the chat",
                        sender:"server",
                        timestamp: Date.now()})
                    })
        }
        socket.on('broadcast', data =>{
            let newList = this.state.messageList.concat([data])
            this.setState({messageList: newList})
        })

    }
    addMessage(object) {
        const array = this.state.messageList
        let newList = array.concat([object])
        this.setState({
            messageList: newList})
    }

    sendMessage(messageString){
      const message = {sender: this.state.username,
            text: messageString,
            timestamp: Date.now()}
        socket.emit('message', message)
        this.addMessage(message)
    }

        render(){
            return(
                <div className="app">
                <MessageList
                    messageList={this.state.messageList}
                    username={this.state.username}
                 />
                <MessageInput
                    sendMessage={i=> this.sendMessage(i)}
                />
                </div>
            )
        }
}

class MessageList extends React.Component{
//USED TO DISPLAY CHAT MESSAGES, WORKS WELL
}


class MessageInput extends React.Component{

    constructor(props){
        super(props)
        this.state = {
            message:''
        }
        this.handleChange = this.handleChange.bind(this)
        this.handleSubmit = this.handleSubmit.bind(this)
    }


    handleChange(event){
        this.setState({
            message: event.target.value
        })
    }

    handleSubmit(event){
        this.props.sendMessage(this.state.message)
        this.setState({
            message:''
        })
    }
    render(){
        return(
            <form
               onSubmit={this.handleSubmit}
               className="send_message_form">
               <input
                   onChange={this.handleChange}
                   value={this.state.message}
                   placeholder="Input a new message"
                   type="text"/>
           </form>
        )
    }
}