Besides what has been suggested, I'd like to post the source code related to SynchronizedMap.
To make a Map thread safe, we can use Collections.synchronizedMap statement and input the map instance as the parameter.
The implementation of synchronizedMap in Collections is like below  
   public static <K,V> Map<K,V> synchronizedMap(Map<K,V> m) {
        return new SynchronizedMap<>(m);
    }
As you can see, the input Map object is wrapped by the SynchronizedMap object.
Let's dig into the implementation of SynchronizedMap , 
 private static class SynchronizedMap<K,V>
        implements Map<K,V>, Serializable {
        private static final long serialVersionUID = 1978198479659022715L;
        private final Map<K,V> m;     // Backing Map
        final Object      mutex;        // Object on which to synchronize
        SynchronizedMap(Map<K,V> m) {
            this.m = Objects.requireNonNull(m);
            mutex = this;
        }
        SynchronizedMap(Map<K,V> m, Object mutex) {
            this.m = m;
            this.mutex = mutex;
        }
        public int size() {
            synchronized (mutex) {return m.size();}
        }
        public boolean isEmpty() {
            synchronized (mutex) {return m.isEmpty();}
        }
        public boolean containsKey(Object key) {
            synchronized (mutex) {return m.containsKey(key);}
        }
        public boolean containsValue(Object value) {
            synchronized (mutex) {return m.containsValue(value);}
        }
        public V get(Object key) {
            synchronized (mutex) {return m.get(key);}
        }
        public V put(K key, V value) {
            synchronized (mutex) {return m.put(key, value);}
        }
        public V remove(Object key) {
            synchronized (mutex) {return m.remove(key);}
        }
        public void putAll(Map<? extends K, ? extends V> map) {
            synchronized (mutex) {m.putAll(map);}
        }
        public void clear() {
            synchronized (mutex) {m.clear();}
        }
        private transient Set<K> keySet;
        private transient Set<Map.Entry<K,V>> entrySet;
        private transient Collection<V> values;
        public Set<K> keySet() {
            synchronized (mutex) {
                if (keySet==null)
                    keySet = new SynchronizedSet<>(m.keySet(), mutex);
                return keySet;
            }
        }
        public Set<Map.Entry<K,V>> entrySet() {
            synchronized (mutex) {
                if (entrySet==null)
                    entrySet = new SynchronizedSet<>(m.entrySet(), mutex);
                return entrySet;
            }
        }
        public Collection<V> values() {
            synchronized (mutex) {
                if (values==null)
                    values = new SynchronizedCollection<>(m.values(), mutex);
                return values;
            }
        }
        public boolean equals(Object o) {
            if (this == o)
                return true;
            synchronized (mutex) {return m.equals(o);}
        }
        public int hashCode() {
            synchronized (mutex) {return m.hashCode();}
        }
        public String toString() {
            synchronized (mutex) {return m.toString();}
        }
        // Override default methods in Map
        @Override
        public V getOrDefault(Object k, V defaultValue) {
            synchronized (mutex) {return m.getOrDefault(k, defaultValue);}
        }
        @Override
        public void forEach(BiConsumer<? super K, ? super V> action) {
            synchronized (mutex) {m.forEach(action);}
        }
        @Override
        public void replaceAll(BiFunction<? super K, ? super V, ? extends V> function) {
            synchronized (mutex) {m.replaceAll(function);}
        }
        @Override
        public V putIfAbsent(K key, V value) {
            synchronized (mutex) {return m.putIfAbsent(key, value);}
        }
        @Override
        public boolean remove(Object key, Object value) {
            synchronized (mutex) {return m.remove(key, value);}
        }
        @Override
        public boolean replace(K key, V oldValue, V newValue) {
            synchronized (mutex) {return m.replace(key, oldValue, newValue);}
        }
        @Override
        public V replace(K key, V value) {
            synchronized (mutex) {return m.replace(key, value);}
        }
        @Override
        public V computeIfAbsent(K key,
                Function<? super K, ? extends V> mappingFunction) {
            synchronized (mutex) {return m.computeIfAbsent(key, mappingFunction);}
        }
        @Override
        public V computeIfPresent(K key,
                BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
            synchronized (mutex) {return m.computeIfPresent(key, remappingFunction);}
        }
        @Override
        public V compute(K key,
                BiFunction<? super K, ? super V, ? extends V> remappingFunction) {
            synchronized (mutex) {return m.compute(key, remappingFunction);}
        }
        @Override
        public V merge(K key, V value,
                BiFunction<? super V, ? super V, ? extends V> remappingFunction) {
            synchronized (mutex) {return m.merge(key, value, remappingFunction);}
        }
        private void writeObject(ObjectOutputStream s) throws IOException {
            synchronized (mutex) {s.defaultWriteObject();}
        }
    }
What SynchronizedMap does can be summarized as adding a single lock to primary method of the input Map object. All method guarded by the lock can't be accessed by multiple threads at the same time. That means normal operations like put and get can be executed by a single thread at the same time for all data in the Map object.  
It makes the Map object thread safe now but the performance may become an issue in some scenarios.   
The ConcurrentMap is far more complicated in the implementation, we can refer to Building a better HashMap for details. In a nutshell, it's implemented taking both thread safe and performance into consideration. 
ConcurrentSkipListMapas another thread-safeMapimplementation. Designed to be highly concurrent under load, using Skip List algorithm. - Basil Bourque