In order to take advantage of the changes in Drupal 7, Views has gone through several API changes.
Here's what you should know.

<h3>Handler registry</h3>

Views now uses Drupal's dynamic-loading code registry.
You can safely remove your implementations of hook_views_handlers(), since they are no longer used.

Please remember to specify the handlers in your module's .info file. For example:
<pre>
name = Example module
description = "Gives an example of a module."
core = 7.x
files[] = example.module
files[] = example.install

; Views handlers
files[] = includes/views/handlers/example_handler_argument_string.inc
</pre>

<h3>Removed handlers</h3>

Note that views_handler_filter_float has been removed.
This functionality is now handled by views_handler_filter_numeric.
There's no need for having a special handler any more, thanks to the new DB layer in Drupal 7.

views_handler_sort_formula has been removed.
Everyone who used it can extend from views_handler_sort, too.

<h3>Ctools dependency</h3>
Views requires ctools now, so it can use the dependency system of ctools.
The only thing you have to do is to replace
<pre>
'#process' => array('views_process_dependency')
</pre>
with
<pre>
'#process' => array('ctools_dependent_process'),
</pre>

<h3>Changed add_where api</h3>
If your field is a plain sql field:
<code>
    $this->query->add_where($this->options['group'], "$this->table_alias.$this->real_field " . $this->operator . " '%s'", $this->value);
</code>
has to be converted to
<code>
    $this->query->add_where($this->options['group'], "$this->table_alias.$this->real_field", $this->value, $this->operator);
</code>
If your field is a complex where condition:
<code>
    $this->query->add_where($this->options['group'], "$upper($field) NOT LIKE $upper('%%%s')", $this->value);
</code>
has to be converted to
<code>
    $placeholder = $this->placeholder();
    $this->query->add_where_expression($this->options['group'], "$field LIKE $placeholder", array($placeholder => '%' . db_like($this->value)));
</code>
placeholder() generates a automatic unique placeholder for you.

add_where with operator 'formula' can be converted to add_where_expression.
add_having with operator 'formula' can be converted to add_having_expression.

<h3>Changed place for display specific settings</h3>
In the new ui the new place for display settings is at the top of the second column.
Therefore use something like this code in your display plugin:
<code>
$categories['block'] = array(
  'title' => t('Block settings'),
  'column' => 'second',
  'build' => array(
    '#weight' => -10,
  ),
);
</code>

<h3>Changed filter settings and associated class variables</h3>
'optional' and 'single' are now 'required' and 'multiple', the logic is now opposite.
Also, the 'no_single' and 'no_optional' class variables (known as "object flags" in the API docs)
are now 'always_multiple' and 'always_required'.