diff --git a/spec/text-editor-component-spec.js b/spec/text-editor-component-spec.js
index 572c42f1f..0366c7415 100644
--- a/spec/text-editor-component-spec.js
+++ b/spec/text-editor-component-spec.js
@@ -901,6 +901,65 @@ describe('TextEditorComponent', () => {
       didDrag(clientPositionForCharacter(component, 4, 10))
       expect(editor.getSelectedScreenRange()).toEqual([[2, 0], [5, 0]])
     })
+
+    it('autoscrolls the content when dragging near the edge of the screen', async () => {
+      const {component, editor} = buildComponent({width: 200, height: 200})
+      const {scroller} = component.refs
+      spyOn(component, 'handleMouseDragUntilMouseUp')
+
+      let previousScrollTop = 0
+      let previousScrollLeft = 0
+      function assertScrolledDownAndRight () {
+        expect(scroller.scrollTop).toBeGreaterThan(previousScrollTop)
+        previousScrollTop = scroller.scrollTop
+        expect(scroller.scrollLeft).toBeGreaterThan(previousScrollLeft)
+        previousScrollLeft = scroller.scrollLeft
+      }
+
+      function assertScrolledUpAndLeft () {
+        expect(scroller.scrollTop).toBeLessThan(previousScrollTop)
+        previousScrollTop = scroller.scrollTop
+        expect(scroller.scrollLeft).toBeLessThan(previousScrollLeft)
+        previousScrollLeft = scroller.scrollLeft
+      }
+
+      component.didMouseDownOnContent({detail: 1, clientX: 100, clientY: 100})
+      const [didDrag, didStopDragging] = component.handleMouseDragUntilMouseUp.argsForCall[0]
+      didDrag({clientX: 199, clientY: 199})
+      assertScrolledDownAndRight()
+      didDrag({clientX: 199, clientY: 199})
+      assertScrolledDownAndRight()
+      didDrag({clientX: 199, clientY: 199})
+      assertScrolledDownAndRight()
+      didDrag({clientX: component.getGutterContainerWidth() + 1, clientY: 1})
+      assertScrolledUpAndLeft()
+      didDrag({clientX: component.getGutterContainerWidth() + 1, clientY: 1})
+      assertScrolledUpAndLeft()
+      didDrag({clientX: component.getGutterContainerWidth() + 1, clientY: 1})
+      assertScrolledUpAndLeft()
+
+      // Don't artificially update scroll measurements beyond the minimum or
+      // maximum possible scroll positions
+      expect(scroller.scrollTop).toBe(0)
+      expect(scroller.scrollLeft).toBe(0)
+      didDrag({clientX: component.getGutterContainerWidth() + 1, clientY: 1})
+      expect(component.measurements.scrollTop).toBe(0)
+      expect(scroller.scrollTop).toBe(0)
+      expect(component.measurements.scrollLeft).toBe(0)
+      expect(scroller.scrollLeft).toBe(0)
+
+      const maxScrollTop = scroller.scrollHeight - scroller.clientHeight
+      const maxScrollLeft = scroller.scrollWidth - scroller.clientWidth
+      scroller.scrollTop = maxScrollTop
+      scroller.scrollLeft = maxScrollLeft
+      await component.getNextUpdatePromise()
+
+      didDrag({clientX: 199, clientY: 199})
+      didDrag({clientX: 199, clientY: 199})
+      didDrag({clientX: 199, clientY: 199})
+      expect(component.measurements.scrollTop).toBe(maxScrollTop)
+      expect(component.measurements.scrollLeft).toBe(maxScrollLeft)
+    })
   })
 })
 
diff --git a/src/text-editor-component.js b/src/text-editor-component.js
index 02e49ecba..0a86629b0 100644
--- a/src/text-editor-component.js
+++ b/src/text-editor-component.js
@@ -14,6 +14,11 @@ const DOUBLE_WIDTH_CHARACTER = '我'
 const HALF_WIDTH_CHARACTER = 'ﾊ'
 const KOREAN_CHARACTER = '세'
 const NBSP_CHARACTER = '\u00a0'
+const MOUSE_DRAG_AUTOSCROLL_MARGIN = 40
+
+function scaleMouseDragAutoscrollDelta (delta) {
+  return Math.pow(delta / 3, 3) / 280
+}
 
 module.exports =
 class TextEditorComponent {
@@ -789,6 +794,7 @@ class TextEditorComponent {
 
     this.handleMouseDragUntilMouseUp(
       (event) => {
+        this.autoscrollOnMouseDrag(event)
         const screenPosition = this.screenPositionForMouseEvent(event)
         model.selectToScreenPosition(screenPosition, {suppressSelectionMerge: true, autoscroll: false})
         this.updateSync()
@@ -835,7 +841,59 @@ class TextEditorComponent {
     window.addEventListener('mouseup', didMouseUp)
   }
 
+  autoscrollOnMouseDrag ({clientX, clientY}) {
+    let {top, bottom, left, right} = this.refs.scroller.getBoundingClientRect()
+    top += MOUSE_DRAG_AUTOSCROLL_MARGIN
+    bottom -= MOUSE_DRAG_AUTOSCROLL_MARGIN
+    left += this.getGutterContainerWidth() + MOUSE_DRAG_AUTOSCROLL_MARGIN
+    right -= MOUSE_DRAG_AUTOSCROLL_MARGIN
+
+    let yDelta, yDirection
+    if (clientY < top) {
+      yDelta = top - clientY
+      yDirection = -1
+    } else if (clientY > bottom) {
+      yDelta = clientY - bottom
+      yDirection = 1
+    }
+
+    let xDelta, xDirection
+    if (clientX < left) {
+      xDelta = left - clientX
+      xDirection = -1
+    } else if (clientX > right) {
+      xDelta = clientX - right
+      xDirection = 1
+    }
+
+    let scrolled = false
+    if (yDelta != null) {
+      const scaledDelta = scaleMouseDragAutoscrollDelta(yDelta) * yDirection
+      const newScrollTop = this.constrainScrollTop(this.measurements.scrollTop + scaledDelta)
+      if (newScrollTop !== this.measurements.scrollTop) {
+        this.measurements.scrollTop += scaledDelta
+        this.refs.scroller.scrollTop += scaledDelta
+        scrolled = true
+      }
+    }
+
+    if (xDelta != null) {
+      const scaledDelta = scaleMouseDragAutoscrollDelta(xDelta) * xDirection
+      const newScrollLeft = this.constrainScrollLeft(this.measurements.scrollLeft + scaledDelta)
+      if (newScrollLeft !== this.measurements.scrollLeft) {
+        this.measurements.scrollLeft += scaledDelta
+        this.refs.scroller.scrollLeft += scaledDelta
+        scrolled = true
+      }
+    }
+
+    if (scrolled) this.updateSync()
+  }
+
   screenPositionForMouseEvent ({clientX, clientY}) {
+    const scrollerRect = this.refs.scroller.getBoundingClientRect()
+    clientX = Math.min(scrollerRect.right, Math.max(scrollerRect.left, clientX))
+    clientY = Math.min(scrollerRect.bottom, Math.max(scrollerRect.top, clientY))
     const linesRect = this.refs.lineTiles.getBoundingClientRect()
     return this.screenPositionForPixelPosition({
       top: clientY - linesRect.top,
@@ -871,11 +929,11 @@ class TextEditorComponent {
     }
 
     if (desiredScrollTop != null) {
-      desiredScrollTop = Math.max(0, Math.min(desiredScrollTop, this.getScrollHeight() - this.getClientHeight()))
+      desiredScrollTop = this.constrainScrollTop(desiredScrollTop)
     }
 
     if (desiredScrollBottom != null) {
-      desiredScrollBottom = Math.max(this.getClientHeight(), Math.min(desiredScrollBottom, this.getScrollHeight()))
+      desiredScrollBottom = this.constrainScrollTop(desiredScrollBottom - this.getClientHeight()) + this.getClientHeight()
     }
 
     if (!options || options.reversed !== false) {
@@ -961,6 +1019,18 @@ class TextEditorComponent {
     return marginInBaseCharacters * baseCharacterWidth
   }
 
+  constrainScrollTop (desiredScrollTop) {
+    return Math.max(
+      0, Math.min(desiredScrollTop, this.getScrollHeight() - this.getClientHeight())
+    )
+  }
+
+  constrainScrollLeft (desiredScrollLeft) {
+    return Math.max(
+      0, Math.min(desiredScrollLeft, this.getScrollWidth() - this.getClientWidth())
+    )
+  }
+
   performInitialMeasurements () {
     this.measurements = {}
     this.measureGutterDimensions()