File and open command in Photoshop and then select the EPS file via your file explorer / browser. Set the width and height for the file and this can be any size, you can linked it so it is proportional but you don't need to, you can set it to 5000 to 2 px etc if you want to seriously squeeze the opened artwork though it will be a pixel / raster design, you cannot open it and use it as a vector (sadly). Set the resolution such as 300 dpi but 72 dpi etc.Set the color mode / image mode to CMYK or RGB or LAB or gray scale.Set anti-aliased to ON (or not).Constrain proportions to ON (or not)) and now you will have a raster layer which can be manipulated using other filters as well as adjustments etc but you cannot modify the points of the shape.
File and open command in Adobe Illustrator and select the vector file in the application. Edit menu and copy and back into Photoshop and then select shape layer. Note that this feature has now been expanded and you can now keep track of the layers. You can now edit the design as a vector and use all the standard tools available in the application.
If the artwork has been copied back into Photoshop (from Illustrator) as a shape layer, you can then save it as a custom shape Go to the toolbar and select the direct selection tool. Select all the points. Goto edit menu. Define custom shape. You can now use the artwork as a vector and as a native custom shape
Go to the place command (linked is probably the best choice). Find the vector file in your files. Click Place embedded or linked. Size as required as well as rotate in current opened document. The design is now a smart object. There are two options, place embedded and place linked. Embedded is great if you are wishing to use a shape you want to be unique to your current work and if you want those edits to the placed file only to be reflected in that file. If you want consistency then the linked is great as any edits to the linked file will be reflected in all files. Of course, other factors may be more important to you such as file size.
Window menu and properties. Select the vector shape. Use the convert to linked (if you used the place embed) and save the artwork to a new file (the embed option means you are not overwriting the original EPS source file). Click edit contents. Edit in Adobe Illustrator. Save to the same file (even though Illustrator persists in setting it to AI by default). If you use the place linked command, you can edit the content via the properties - simply click the edit contents button in the layer panel (though this does require the association to be set correctly otherwise a totally different application will open such as the preview application on the mac - you will have to use the open with command to re-associate the file).
File place (linked) command into the application and browse for the files and click place.size as required. Go to the layers panel and double click the small smart object icon or go to the right side menu and use edit contents and then modify the design in Adobe Illustrator. and then file save. You can also use the smart objects menu command and the edit contents command (found in the layers panel menu or smart objects menu in layer menu) or just double clicking the thumbnail. The result is opened in Adobe Illustrator