Select some text and then go to the object menu and then to the envelope distort category and make with warp command. You can use it with live or expanded if you wish. It is live it means you can always edit the characters and update the contents at a later time via the envelope menu commands. You distort a single letter as well as many letters and also a whole page if you wish.
Set style to arc, wave, fish etc and set horizontal or vertical and set bend value to subtle or max (100%) settings to totally modify the text and to bend it the other way, set it to -100%. Set the direction of the bend, by default, horizontal but vertical creates an interesting effect also. The distortion setting squeezes it at one end, set to the max and you will have a smaller left than right side or set it to -100% you will have a smaller right side than left (if using horizontal). Set the preview to ON. Click OK. With the envelope object selected, you will also notice that the controls to modify the bend etc are available in the control bar. Youtube video on subject
You can then just keep with the envelope or expand the envelope via the expand command in the object menu. If not expanded, the object is still live so the envelope can still be modified by just using tools such as the direct selection tool where the envelope points can be selected and then dragged to further modify the text and this can be used to create ever more complex designs. You can also right click and select isolation mode and then you can edit the words, you can do the same via the edit envelope command found in the object menu.
Select some text and go to the object menu and make with mesh command. Set the number of rows and columns for the warp mesh, the default 4 x 4 but it can be 20 x 20 etc. Click OK. Go to the toolbar and select the direct selection tool and then click on the individual points or select multiple points on the mesh with the tool and then drag to stretch the characters. You can also stretch them by clicking on the anchor points and lengthening and rotating those anchors.
Go to the object menu and envelope and expand. The envelope and text are no longer live but you can now edit it as a normal path using direct selection tool etc
Create some characters and then go to the toolbar and select one of the shape tools or use the pen tool and create a new shape and this will be the top object. Select both objects and then go to the object menu and envelope and top object. No panel etc appears. You can now manipulate the text using the direct selection tool by selecting the points of the envelope as well as the anchor points and handles. Youtube video on subject
There are a variety of warp tools available such as the crystallize tool and the wrinkle tool, scallop and others. The object needs to be expanded first via the object menu and expand. It is a destructive effect. Go to the crystallize tool (for example) and double click to display the options such as the width and height of the tool and then apply the crystallize effect to the characters and drag and distort the designs in all kinds of ways.
Wrinkle, Youtube video on subject
Crystallize, Youtube video on subject
Scallop, Youtube video on subject
You can also combine this with the powerful repeat radial feature with the object and continue to manipulate the object inside the repeat object to create an infinite number of radial designs. You can find this feature in the object menu and repeat and radial or grid etc. Youtube video on subject
You can also use the free distort effect found in the effects menu. Select the object, expanded or not and then use the effect. The panel is small, it has not been updated for ages and ages and it sometimes can be slightly frustrating to use in that clicking sometimes results in no action at all and then suddenly it will work and modify the object in the preview. You can apply it once or multiple times but they will be available via the appearance panel. You can also apply it to a new fill or the fill alone or apply it to the stroke as well as a new stroke and you can create multiple of those in different colors etc and they can all be transformed using this feature so you can create quite complex designs in seconds using this feature. As it is a live effect, you can also save all of this to the graphic styles panel for future use with other letters etc. It can be distorted in countless ways and you can create stunning artwork. Once you are happy with your design you can always expand the entire object by going to the object menu and expand appearance. Youtube video on subject