Home page of their website -  the site contains lots of useful information (a few are shown below), and also numerous forms that can be used to report something eg illegally parks cars, street lighting faults, missed bin collections, overhanging trees and many many more.
To report anything for which you cannot find a form or to contact CEC for anything else email customer.care@edinburgh.gov.uk  

Road Disruptions - locations and dates for roadworks and traffic disruptions 

Consultation Hub - topics being considered for Edinburgh which you may wish to comment on 

Paying for a Care Home - information about care home charges and paying for them

Longstone     Hutchison Chesser     Morningside    Merchiston     Firrhill 

Colinton and the Colinton Amenity Association

Contact the Police Scotland Community Team email EdinburghCPTSouthWest@Scotland.pnn.police.uk

Sign up to Neighbourhood Watch Alerts 

Edinburgh Police on Facebook and Twitter 

If you required advice or to report a crime phone 101 or 999 if an emergency.

Local Councillors and Members of Parliament 

Report Graffiti and Damage - information we have pulled together to let you know who to report it to.

Overhanging Foliage eg Trees, hedges, bushes - how far back hedges, trees etc should be cut -
https://www.gardeningdata.co.uk/shrubs/hedges_and_roads/hedge_trim_highway.php 
If overhanging foliage is a problem it can be raised directly with the owner of the relevant property. 
If this is not appropriate or does not work then it can be reported on the CEC website - https://www.edinburgh.gov.uk/overhangingfoliage